From owner-philofractal@icd.com Mon Mar 1 00:42:17 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA12955 for philofractal-list; Sun, 28 Feb 1999 23:42:43 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from yuma.ACNS.ColoState.EDU (root@yuma.ACNS.ColoState.EDU [129.82.100.64]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA12825 for ; Sun, 28 Feb 1999 23:11:33 -0600 Received: from holly.colostate.edu (res099037.HALLS.ColoState.EDU [129.82.99.37]) by yuma.ACNS.ColoState.EDU (AIX4.3/UCB 8.8.8/8.8.8) with ESMTP id WAA137426 for ; Sun, 28 Feb 1999 22:13:48 -0700 Message-ID: <36DA220A.516F4F6E@holly.colostate.edu> Date: Sun, 28 Feb 1999 22:13:46 -0700 From: Xylen X-Mailer: Mozilla 4.5 [en] (Win95; U) X-Accept-Language: en MIME-Version: 1.0 To: "philofractal@icd.com" Subject: [philofractal] Alice Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com I don't remember who posted first about Alice In Wonderland, but it got me to thinking. Was Alice the first fractal explorer? Falling down the rabbit hole sure sounds a lot like deep zooming into a fractal. I wonder, what other fractal like references are in that story? Hmm, I may have to re-read it again. Xylen -- ----------------------------------------------------------------------- "I've been placed on this world to accomplish a certain number of things. Right now I am so far behind, I will never die" http://members.tripod.com/~Xylen Fight Spam! Join CAUCE! == http://www.cauce.org/ ----------------------------------------------------------------------- _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Mon Mar 1 01:42:09 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA13199 for philofractal-list; Mon, 1 Mar 1999 00:42:02 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from camel7.mindspring.com (camel7.mindspring.com [207.69.200.57]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA13124 for ; Mon, 1 Mar 1999 00:28:51 -0600 Received: from LOCALNAME (user-2iveial.dialup.mindspring.com [165.247.73.85]) by camel7.mindspring.com (8.8.5/8.8.5) with SMTP id BAA22322 for ; Mon, 1 Mar 1999 01:31:06 -0500 (EST) Date: Mon, 1 Mar 1999 01:31:06 -0500 (EST) Message-Id: <1.5.4.16.19990301013057.2b47d4d8@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 01-03-99 (Polarized Figure) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 01, 1999 Fractal enthusiasts: Here it is -- the first day of the third month of the last year of the second millennium. Purists might point out that the year 2000 is actually the last year of the second millennium, but to all but the purest purists, the big day will be January 01, 2000. In honor of today's non-event, it rained all day. The tempera- ture of 46F 8C was a bit too chilly for outdoor comfort, but it was perfect for hunting fractals. And how I hunted! Determined to resist the temptation to copy the critical.frm file with its seven MandelbrotMix formulas back into my Fractint directories, so I could search for more midgets, I turned to my all-purpose jim.frm file, and dredged up a formula named TowerMinExp02. Surprisingly, with all parameters set to zero, this formula draws a rather interesting default scene. Today's picture is a zoom into one of many areas of interest in this fractal. I have named the picture "Polarized Figure" because at its center, it reminds me of a vague blue and yellow figure that appears at the center of my field of vision whenever I look through a polarizing filter at a featureless background, such as a blank wall, and rotate the filter. I have no idea what causes this figure, but it is always there when I gaze at a featureless source of polarized light, such as a deep blue sky at 90 degrees from the sun, where I can see it even without a polarizing filter. I realize that the human eye is generally unable to detect the polarization of light without some kind of instrument, so I assume that my eyes are somehow out of the ordinary. I believe that certain birds are able to navigate by detecting the polarization of the sky's light, so my ability might not be so unusual after all. But it is interesting to note that, to my knowledge, if the human eye does have this vestigial ability, it has so far failed to be noticed. But today's fractal picture is one to be noticed. It is actu- ally a Julia set of the formula Z=Z^(-Z^Z)+C, where the constant of C is zero. The lacy, fern-like shapes form a rough figure-8 of concentric rings, growing ever smaller as they approach the central open area. The parameter file runs in 15 minutes, but if this tries your patience, the GIF file has been posted to: and to: Now I must catch up on today's mail. I see that Dr. J is back, and I want to check what he's been up to. So until next time, which will come in 24 hours, take care, and wouldn't it be surprising if the answer to the riddle of the universe were to be found in a fractal? Jim Muth jamth@mindspring.com START FORMULA============================================= TowerMinExp02 {; Jim Muth z=pixel, c=p2+(p3*pixel): z=z^(-z^(z+p1))+c, |z| <= 100 } END FORMULA=============================================== START PARAMETER FILE====================================== Polarized_Figure { ; 16min on a 486-100mhz, 640x480 ; Version 1961 Patchlevel 40 reset=1961 type=formula formulafile=jim.frm formulaname=TowerMinExp02 passes=1 center-mag=0.982365/-0.000713437/3.875969/1/29.999 params=0/0/0/0/0/0 float=y maxiter=500 bailout=25 inside=bof61 logmap=yes symmetry=none periodicity=10 colors=000FYP<3>0AC<5>mO7c_bvDv<7>87W<4>NLUPNURPV\ <10>slg<8>qqTqqSnpU<16>Cks<23>v8W<14>hSyhTzfUv<16>H\ f6Ac0<8>tzK<5>`tWXw`<10>`O5<7>eNRfNzfNX<9>lMwVHjlMy\ <15>TlrMYOSmr<9>_Jb`B`<8>Ync<15>OSSSSX<6>5O3<13>OXW\ Uvb<2>IcS } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Polarized_Figure { ; 16min on a 486-100mhz, 640x480 ; Version 1961 Patchlevel 40 reset=1961 type=formula formulafile=jim.frm formulaname=TowerMinExp02 passes=1 center-mag=0.982365/-0.000713437/3.875969/1/29.999 params=0/0/0/0/0/0 float=y maxiter=500 bailout=25 inside=bof61 logmap=yes symmetry=none periodicity=10 colors=000FYP<3>0AC<5>mO7c_bvDv<7>87W<4>NLUPNURPV\ <10>slg<8>qqTqqSnpU<16>Cks<23>v8W<14>hSyhTzfUv<16>H\ f6Ac0<8>tzK<5>`tWXw`<10>`O5<7>eNRfNzfNX<9>lMwVHjlMy\ <15>TlrMYOSmr<9>_Jb`B`<8>Ync<15>OSSSSX<6>5O3<13>OXW\ Uvb<2>IcS } frm:TowerMinExp02 {; Jim Muth z=pixel, c=p2+(p3*pixel): z=z^(-z^(z+p1))+c, |z| <= 100 } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue Mar 2 00:42:06 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA20100 for philofractal-list; Mon, 1 Mar 1999 23:42:20 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from blue.hermes.net.au (blue.hermes.net.au [203.35.8.194]) by rock.icd.com (8.9.1/8.9.1) with SMTP id XAA19969 for ; Mon, 1 Mar 1999 23:10:07 -0600 Received: from narada (unverified [203.35.207.178]) by blue.hermes.net.au (EMWAC SMTPRS 0.83) with SMTP id ; Tue, 02 Mar 1999 16:10:11 +1100 Message-ID: <002b01be646d$2a479620$b2cf23cb@narada> From: "narada" To: Subject: [philofractal] Amusement park ride? Date: Tue, 2 Mar 1999 16:20:41 +1100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.2106.4 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.2106.4 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com As one zooms in on a mandelbrot it's akin to a landing descent onto an infinitely distant and infinitely large planet. How about a room in which one is suspended above a floor upon which is projected somehow an image of the mandelbrot which one "falls towards". One could also perhaps 'hover', move sideways, or back out too. Surely we have the technology to do this already. If the walls were also screens then the room would not have to be enormous to give the illusion of size. Any entreprenuers interested? _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue Mar 2 00:42:07 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA20111 for philofractal-list; Mon, 1 Mar 1999 23:42:50 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from blue.hermes.net.au (blue.hermes.net.au [203.35.8.194]) by rock.icd.com (8.9.1/8.9.1) with SMTP id XAA19967 for ; Mon, 1 Mar 1999 23:10:04 -0600 Received: from narada (unverified [203.35.207.178]) by blue.hermes.net.au (EMWAC SMTPRS 0.83) with SMTP id ; Tue, 02 Mar 1999 16:10:10 +1100 Message-ID: <002a01be646d$2954f8c0$b2cf23cb@narada> From: "narada" To: Subject: [philofractal] Non static patterns Date: Tue, 2 Mar 1999 16:17:26 +1100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.2106.4 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.2106.4 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Has anyone worked out formulas for fractals that are not static over time? I dont mean patterns in time like stock market fluctuations etc, I mean mandelbrots that have some parameter that changes value over time such that the pattern itself morphs. (I know there are formulas that use the iteration count to change the result for each point but thats a different thing too.) All 3 dimensional fractals could I suppose be considered to be 2D ones that change in the teporal axis. Has anyone ever animated the 2D cross-sections of a 3D fractal? It seems to me that this would add a new dimension to their metaphorical beauties. Best Wishes All Ways N _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue Mar 2 00:42:07 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA20115 for philofractal-list; Mon, 1 Mar 1999 23:42:52 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from blue.hermes.net.au (blue.hermes.net.au [203.35.8.194]) by rock.icd.com (8.9.1/8.9.1) with SMTP id XAA19965 for ; Mon, 1 Mar 1999 23:09:57 -0600 Received: from narada (unverified [203.35.207.178]) by blue.hermes.net.au (EMWAC SMTPRS 0.83) with SMTP id ; Tue, 02 Mar 1999 16:10:08 +1100 Message-ID: <002901be646d$285933a0$b2cf23cb@narada> From: "narada" To: Subject: [philofractal] These words do not mean what you think they mean... Date: Tue, 2 Mar 1999 16:12:13 +1100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.2106.4 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.2106.4 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com There is no why or wherefore No birds in the sky and therefore I must try to be more careful what I say. What I say means nothing, Its just a horse I'm riding, and today I'm just in time to catch the last rays of the sun and that's enough to keep me going till I get there. ******* ('Meaning' is the primal substance of all existance. Space, time, energy, matter,mind,etcetera, are all modes of expression of Meaning. Meaning cannot be bound within any language, for all languages are themselves but metaphors for the inexpressible core of Meaning. Mind cannot encompass Meaning, but only immerse itself in the radiant depths of transmutative mystery such that its every thought directs it deeper into what IS.) Best Wishes All Ways N _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue Mar 2 00:42:07 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA20119 for philofractal-list; Mon, 1 Mar 1999 23:42:54 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from blue.hermes.net.au (blue.hermes.net.au [203.35.8.194]) by rock.icd.com (8.9.1/8.9.1) with SMTP id XAA19971 for ; Mon, 1 Mar 1999 23:10:11 -0600 Received: from narada (unverified [203.35.207.178]) by blue.hermes.net.au (EMWAC SMTPRS 0.83) with SMTP id ; Tue, 02 Mar 1999 16:10:14 +1100 Message-ID: <002c01be646d$2b4afc60$b2cf23cb@narada> From: "narada" To: Subject: Re: [philofractal] Musings on four questions - possibly irrelevant aside. Date: Tue, 2 Mar 1999 16:24:42 +1100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.2106.4 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.2106.4 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com >>>With all this scientific uncertainty, isn't it a bit premature >>>to state, "God does not exist", and use the discoveries of >>>science to support such a statement? >> >>Yes, I agree. But because of my earlier statement that science is also a >>religion, this should not be a surprise ... (:->) >> >I still don't think that science can be called a religion. To me, a >religion necessarily has some element of the supernatural (beyond nature) >in its credo. Science, by what passes for a definition, doesn't. This is >why I can put a case for "Mathematics is a religion" when I feel like it - >I don't consider mathematics to be a science; and I can claim that the >Platonic Realm of Mathematics is real just as vociferously as a devout >Catholic can about God. There's more detail, but I'm not in a mood to give >it - Maths is an art I tell ye! :-) You know the funny thing about religions, (and I have tried a few of them), is that they all have a reason why they dont consider themselves to be in the class of 'religion'. Basically they all think they have the TRUTH, and that the other systems are lacking in this that or the other. "Scientific Materialism" is I believe the dominant religion on this planet at this time. It has infiltrated and subsumed most previous religions, and is so universally accepted that most of its adherents are unaware that it is a belief system, let alone a religion! They simply believe that they are studying the TRUTH. The Hindus for instance also claim not to be a religion, and they have a wonderful term for their belief system. They call it the Sanatana Dharma, the eternal truth. (And they have a cosmology that involves multidimensional universes, and spans of time far greater than our... how many billion years?) I do appreciate that some of the voices here have travelled the path of scientific materialism a considerable distance, and have gleaned much wisdom and insight into the nature of their own reality from the disciplines and practices of their creed. Such is the gift that a true religion bestows upon its adherents. Therefore Oh venerable sages, please have patience with this foolish neophytes musings, he does not mean to slip into the heresies of psuedoscience, but is merely inexperienced in the approriate metaphorical systems of the standard model. OK. So as a separate question regards measures etc... let me throw in some wild ideas- Speed is considered to be relative to the observational referance point, but is their any meaning to size, duration, and amount of energy, except in comparison to another quantity of the same? Also, is 'shape' a relative phenomena in the sense that something is curved only in referance to another part of itself? Normally one thinks that if space becomes 'curved' enough it reaches its limit when it turns 360 degrees and closes on itself spherically, but what if space were curved like a fractal spiral? What if it curved in x many dimensions but remained 'open' in others? Best Wishes All Ways N _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue Mar 2 02:42:00 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id BAA20620 for philofractal-list; Tue, 2 Mar 1999 01:42:02 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp2.mindspring.com (smtp2.mindspring.com [207.69.200.32]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id BAA20498 for ; Tue, 2 Mar 1999 01:07:22 -0600 Received: from LOCALNAME (user-2ivei2i.dialup.mindspring.com [165.247.72.82]) by smtp2.mindspring.com (8.8.5/8.8.5) with SMTP id CAA27017 for ; Tue, 2 Mar 1999 02:09:08 -0500 (EST) Date: Tue, 2 Mar 1999 02:09:08 -0500 (EST) Message-Id: <1.5.4.16.19990302020853.2b47e086@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 02-03-99 (This is a Blivot) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 02, 1999 Fractal enthusiasts: Today was raw and windy with occasional sprinkles of snain and a temperature of 41F 5C. It was perfect for hunting fractals, of course, but that's not saying much, since every day is perfect for hunting fractals. For today's non-midget fractal, I chose a test formula -- number 14 of a series of 58 test formulas in the jim.frm file. I have no idea what I was testing when I wrote it, but it resembles the formulas in my MandNewt series. Unfortunately, I have no idea what the MandNewt series was designed to do, so this is no help. I named the curious fractal picture "This is a Blivot", because that's just what it is. Blivot is the word I use to describe an apparent 3-D object that can be drawn on a two-dimensional sheet of paper, but cannot exist in a three dimensional space. That great mathematical artist, M.C.Escher filled his drawings with thinly-disguised blivots, which appear as absurdities such as impossible buildings and waterfalls, and a procession of monks that climbs a circular staircase which, though it constantly leads upward, never goes anywhere. The picture is not one of a blivot, it is a picture of a fractal -- a fractal which draws in 12 minutes on a 486 and much faster on a Pentium. And if that's not fast enough, the GIF file has been posted to Usenet at: and to the FOTD web site at: I read recently on the Philofractal list that science differs from religion in that science does not admit the existence of the supernatural, while religion does. The way I see it, science constantly confirms the existence of the supernatural, though when it discovers the supernatural, science no longer considers it supernatural. Actually, by definition, the supernatural is impossible. But all is not lost. The world is filled with the unknown, which seems supernatural until it is understood, at which time it becomes perfectly natural. 150 years ago, seeing what is happening on the opposite side of the world at the same time as it happens would have been considered supernatural. Today this supernatural event happens all the time. It is the perfectly natural thing known as television. Today, things such as mental telepathy are considered super- natural, but when and if they are is detected scientifically, they will be seen to operate by natural laws. The happenings will then be considered natural. This is how human knowledge grows. So until we meet again naturally, take care, and gain infinite knowledge from a fractal. Jim Muth jamth@mindspring.com START FORMULA============================================= Test14 {; Jim Muth z=c=pixel: a=z^3+(c-p2)*z-c b=p1*z^2+c-1 z=z-1*a/b p3 <= |a| } END FORMULA=============================================== START PARAMETER FILE====================================== This_is_a_Blivot {; 12min on a 486-100, 640x480 reset=1960 type=formula formulafile=jim.frm formulaname=Test14 passes=t center-mag=-0.277717/-0.0953073/0.4536489 params=0.48/4.34/-0.62/-1.62/2.13/4.43 float=y maxiter=500 bailout=25 inside=255 logmap=yes symmetry=none periodicity=10 colors=000`FE<4>RC1PG2NJ2<8>kk2<8>vbAfiJ<7>7Q\ q<3>L8z<8>dKIfLDgLE<5>mLK<5>AZ1<4>KgeQkdVnd\ <11>rBk<13>FVT<2>B1V<10>X20<7>RcJRgLSbP<5>XEl\ <10>ejSemRenS<12>eoX<2>fDD<5>NCH<14>eIl<5>S6z\ QHm<6>Baj9dj8ef<11>8h2<12>pKdsCeu4e<8>D5M<2>N\ kFFn5XlHmjT<3>gYX<6>XroWuqTmhRe`pLW<5>ZGG0Uu } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= This_is_a_Blivot {; 12min on a 486-100, 640x480 reset=1960 type=formula formulafile=jim.frm formulaname=Test14 passes=t center-mag=-0.277717/-0.0953073/0.4536489 params=0.48/4.34/-0.62/-1.62/2.13/4.43 float=y maxiter=500 bailout=25 inside=255 logmap=yes symmetry=none periodicity=10 colors=000`FE<4>RC1PG2NJ2<8>kk2<8>vbAfiJ<7>7Q\ q<3>L8z<8>dKIfLDgLE<5>mLK<5>AZ1<4>KgeQkdVnd\ <11>rBk<13>FVT<2>B1V<10>X20<7>RcJRgLSbP<5>XEl\ <10>ejSemRenS<12>eoX<2>fDD<5>NCH<14>eIl<5>S6z\ QHm<6>Baj9dj8ef<11>8h2<12>pKdsCeu4e<8>D5M<2>N\ kFFn5XlHmjT<3>gYX<6>XroWuqTmhRe`pLW<5>ZGG0Uu } frm:Test14 {; Jim Muth z=c=pixel: a=z^3+(c-p2)*z-c b=p1*z^2+c-1 z=z-1*a/b p3 <= |a| } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue Mar 2 13:42:11 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id MAA24101 for philofractal-list; Tue, 2 Mar 1999 12:42:14 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp2.mindspring.com (smtp2.mindspring.com [207.69.200.32]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id MAA23983 for ; Tue, 2 Mar 1999 12:28:26 -0600 Received: from LOCALNAME (user-2iveiat.dialup.mindspring.com [165.247.73.93]) by smtp2.mindspring.com (8.8.5/8.8.5) with SMTP id NAA11885 for ; Tue, 2 Mar 1999 13:30:08 -0500 (EST) Date: Tue, 2 Mar 1999 13:30:08 -0500 (EST) Message-Id: <1.5.4.16.19990302132953.2b6fbd2a@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] Musings on narada's musings Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 04:24 PM 3/2/99 +1100, narada wrote: >"Scientific Materialism" is I believe the dominant religion on >this planet at this time. It has infiltrated and subsumed most >previous religions, and is so universally accepted that most of >its adherents are unaware that it is a belief system, let alone >a religion! They simply believe that they are studying the >TRUTH. Well stated and very true! Consider the most basic premise of modern science -- there was material before there was mind; there were events before there were minds to perceive those events. This is the philosophy of materialism. It is the premise that supports the entire method of modern science, yet true or not, it is as much an article of faith as any doctrine of conventional religion. If science had an official creed, it would read somewhat as follows: "In the name of material reality, we need only to continue implementing those rational values that have brought our planet to its present enlightened state. When false science disappears and true science prevails, scientific progress will take over and eventually bring a paradise on earth, where those alive at the time will exist in perfect happiness." >I do appreciate that some of the voices here have travelled the >path of scientific materialism a considerable distance, and >have gleaned much wisdom and insight into the nature of their >own reality from the disciplines and practices of their creed. >Such is the gift that a true religion bestows upon its >adherents. I am one of those who has travelled far into scientific materialism. And over the years that I have been travelling, I have gradually come to realize that science has many aspects. In one aspect, it is indeed just another religion -- my chosen religion -- the religion that currently happens to be the world's most widespread religion. If this were not so, why would this obvious fact be denied with such religious zealotry by so many. >Therefore Oh venerable sages, please have patience with this >foolish neophytes musings, he does not mean to slip into the >heresies of psuedoscience, but is merely inexperienced in the >approriate metaphorical systems of the standard model. Don't feel heretical if you find some pseudoscience interesting and not easily cast aside. As I wrote in my most recent FOTD, the pseudoscience of one century can become the true science of the next century. Next FOTD in 12 hours or so. Jim Muth jamth@mindspring.com _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 3 00:43:22 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA27337 for philofractal-list; Tue, 2 Mar 1999 23:42:01 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from camel8.mindspring.com (camel8.mindspring.com [207.69.200.58]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA27331 for ; Tue, 2 Mar 1999 23:41:06 -0600 Received: from LOCALNAME (user-2iveike.dialup.mindspring.com [165.247.74.142]) by camel8.mindspring.com (8.8.5/8.8.5) with SMTP id AAA25065 for ; Wed, 3 Mar 1999 00:42:43 -0500 (EST) Date: Wed, 3 Mar 1999 00:42:43 -0500 (EST) Message-Id: <1.5.4.16.19990303004221.290f2688@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 03-03-99 (Mandelbrot or Julia) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 03, 1999 Fractal enthusiasts: Today was a perfect late Winter day here at Fractal Central. The brilliant sun, blue sky and mild 50F 10C temperature were perfect for walking and also for fractalling. I did both. They say that walking increases the blood flow to the brain and aids the thought processes. If that is the case, my thinking must be in top form, because I walked over 6km this afternoon. As I walked, watching the squirrels doing unmentionable things, my thoughts drifted from pondering the science-religion topic to visualizing three-dimensional slices of the four-dimensional Z^2+C Julibrot object. There are four perpendicular 3-D slices through any point of a 4-D object, and an infinity of oblique 3-D slices. I have condensed this infinity of oblique slices into 24 slices at 45 degree angles to the perpendiculars. I know the shape of the perpendicular 3-D slices fairly well, but the 45-degree slices, many of which are similar, are still quite vague. One of my favorite mental tricks is rotating the whole Julibrot around one of its six perpendicular planes. In four dimensions, rotation takes place around an axis plane, just as rotation takes place around an axis line in 3-D space. Unfortunately, due to our conceptual limitations, this four-dimensional rotation cannot be seen in the 3-D space that is the highest space we can visualize. But interesting parts of the rotation can be seen in 3-D space, their exact nature depending on how the axis-plane of the 4-D object is oriented in respect to our 3-space. If the axis plane is perpendicular to our space, only a single line of it will exist in our space, and we will see an odd-shaped 3-D object rotating in space around its axis-line in the normal manner. If the axis plane is at an oblique angle to our space, only a single line of it will exist in our space. But in this case, different parts of the rotating 4-D object will pass through our space, and we will see an object changing shape before our eyes. Many computer animations of such a rotation have been done. If the axis plane lies within our space, all points of the plane will remain fixed in position as the 4-D object rotates. We will see an object changing shape more rapidly and radically at the points farthest from the axis plane, and more slowly nearer the plane. In the axis plane itself, no change will take place, even though every point in the entire plane is rotating on itself. A four-dimensional object may also rotate around two axis planes simultaneously. This is known as a double rotation, and in this case, only a single point of the object remains fixed in position, while if both rotations are equal, every other point moves in a circle. Today's picture illustrates such a double rotation. I have named today's picture "Mandelbrot or Julia", though actually it is neither. It is an image of a slice through the Julibrot at an angle halfway through the double rotation between the Mandelbrot and Julia directions. It happens to be my favorite oblique slice through the origin of the Julibrot, other than the Mandelbrot set itself. The parameter file runs spectacularly fast, requiring only a second or two on a Pentium. But if even this isn't fast enough, the GIF file has been posted in all its emerald glory to: and to: I'll return tomorrow with more fractal news and another fractal image. Until then, take care, and don't get double-rotated right out of our three-space. Jim Muth jamth@mindspring.com START FORMULA============================================= multirot-XY-ZW {; draws 6 planes and many rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(z)+c, |z| <= 36 } END FORMULA=============================================== START PARAMETER FILE====================================== Mandlbrot_or_Julia { ; 5sec on a 486-100, 640x480 reset=1960 type=formula formulafile=multirot.frm formulaname=multirot-XY-ZW function=ident/flip center-mag=-0.553341/0/0.4976526 params=-45/45/0/0/0/0 float=y maxiter=240 bailout=25 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000DLA<5>8mGCpH<2>OxRRzZSwfSulTsrTqz<2>VjzVh\ zXdz<5>cHzdDzgEz<5>sGzN2z5`z<5>RWz<2>wtz<4>Pjz<3>9z\ z<4>uiz<5>DDz<5>Edz<7>bBzl_zuxz<3>35z<2>etz<3>hcz\ <7>7ozoaz<2>23z<6>D0zE0zH6z<2>OLz<2>9xz<3>a1z<2>y2z\ <6>8kz<2>LOzadzqtz6Mz<2>mVzjfzhrz<7>uqz<3>VMzHcz4uz\ <4>5Dz<2>x0z<7>A7z<7>PNz<3>1kz<3>YIz`Iz<3>MkzJrzHNz\ <6>xLz<4>8szk6z<6>dBzdBzeBz<9>kAzlAznAzmAzmAznAzgMz\ <16>lEzFWzEQz } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Mandlbrot_or_Julia { ; 5sec on a 486-100, 640x480 reset=1960 type=formula formulafile=multirot.frm formulaname=multirot-XY-ZW function=ident/flip center-mag=-0.553341/0/0.4976526 params=-45/45/0/0/0/0 float=y maxiter=240 bailout=25 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000DLA<5>8mGCpH<2>OxRRzZSwfSulTsrTqz<2>VjzVh\ zXdz<5>cHzdDzgEz<5>sGzN2z5`z<5>RWz<2>wtz<4>Pjz<3>9z\ z<4>uiz<5>DDz<5>Edz<7>bBzl_zuxz<3>35z<2>etz<3>hcz\ <7>7ozoaz<2>23z<6>D0zE0zH6z<2>OLz<2>9xz<3>a1z<2>y2z\ <6>8kz<2>LOzadzqtz6Mz<2>mVzjfzhrz<7>uqz<3>VMzHcz4uz\ <4>5Dz<2>x0z<7>A7z<7>PNz<3>1kz<3>YIz`Iz<3>MkzJrzHNz\ <6>xLz<4>8szk6z<6>dBzdBzeBz<9>kAzlAznAzmAzmAznAzgMz\ <16>lEzFWzEQz } frm:multirot-XY-ZW {; draws 6 planes and many rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(z)+c, |z| <= 36 } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 3 04:42:06 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id DAA28271 for philofractal-list; Wed, 3 Mar 1999 03:42:05 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id DAA28144 for ; Wed, 3 Mar 1999 03:18:20 -0600 Received: from packrat.nznet.gen.nz (ms2-56.nznet.gen.nz [203.167.232.186]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id WAA18661 for ; Wed, 3 Mar 1999 22:19:22 +1300 Message-Id: <3.0.3.32.19990303221226.006ea530@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Wed, 03 Mar 1999 22:12:26 +1300 To: philofractal@icd.com From: "Morgan L. Owens" Subject: Re: [philofractal] Musings on narada's musings In-Reply-To: <1.5.4.16.19990302132953.2b6fbd2a@pop.mindspring.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 13:30 02/03/99 -0500, Jim wrote: > >Don't feel heretical if you find some pseudoscience interesting >and not easily cast aside. As I wrote in my most recent FOTD, >the pseudoscience of one century can become the true science of >the next century. > But don't go claiming that it's scientific _yet_. If you're going to do that you might as well try entering a jetboat in the next America's Cup - because the Cup rules might be changed to allow jetboats in the future. Morgan L. Owens _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 3 04:42:06 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id DAA28275 for philofractal-list; Wed, 3 Mar 1999 03:42:29 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id DAA28143 for ; Wed, 3 Mar 1999 03:18:19 -0600 Received: from packrat.nznet.gen.nz (ms2-56.nznet.gen.nz [203.167.232.186]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id WAA18656 for ; Wed, 3 Mar 1999 22:19:20 +1300 Message-Id: <3.0.3.32.19990303221620.006eb538@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Wed, 03 Mar 1999 22:16:20 +1300 To: philofractal@icd.com From: "Morgan L. Owens" Subject: Re: [philofractal] Musings on four questions - possibly irrelevant aside. In-Reply-To: <002c01be646d$2b4afc60$b2cf23cb@narada> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 16:24 02/03/99 +1100, narada wrote: > >You know the funny thing about religions, (and I have tried a few of them), >is that they all have a reason why they dont consider themselves to be in >the class of 'religion'. Basically they all think they have the TRUTH, and >that the other systems are lacking in this that or the other. "Scientific >Materialism" is I believe the dominant religion on this planet at this time. >It has infiltrated and subsumed most previous religions, and is so >universally accepted that most of its adherents are unaware that it is a >belief system, let alone a religion! They simply believe that they are >studying the TRUTH. > They believe they are studying _reality_ - Science makes no official claims as to the _truth_ of its ideas. And if what they're studying is not reality, they'd like to know what the hell is. Science doesn't offer absolutes; sorry. If you want those you'll have to go elsewhere. And Mathematics doesn't offer truth either; sorry. Alfred Tarski mathematically proved as much in 1933. > >I do appreciate that some of the voices here have travelled the path of >scientific materialism a considerable distance, and have gleaned much wisdom >and insight into the nature of their own reality > Which would have to be the same as everyone else's, otherwise we're not talking about reality. > Also, is 'shape' a relative phenomena in the sense that something is curved >only in referance to another part of itself? Normally one thinks that if space >becomes 'curved' enough it reaches its limit when it turns 360 degrees and >closes on itself spherically, but what if space were curved like a fractal >spiral? What if it curved in x many dimensions but remained 'open' in others? > Ah, now there you're getting into metric topology, where curvature becomes irrelevant to defining the object - a field of mathematics which happens to include much of the study of fractals within it! Morgan L. Owens "The truth is whatever you can't escape." Greg Egan, _Distress_ (Very relevant to this thread - highly recommended). _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 3 04:42:17 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id DAA28279 for philofractal-list; Wed, 3 Mar 1999 03:42:30 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id DAA28142 for ; Wed, 3 Mar 1999 03:18:18 -0600 Received: from packrat.nznet.gen.nz (ms2-56.nznet.gen.nz [203.167.232.186]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id WAA18644 for ; Wed, 3 Mar 1999 22:19:18 +1300 Message-Id: <3.0.3.32.19990303221631.006e3f58@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Wed, 03 Mar 1999 22:16:31 +1300 To: philofractal@icd.com From: "Morgan L. Owens" Subject: Re: [philofractal] Musings about metaphors, modelling, etc In-Reply-To: <001a01be630d$2d826ec0$a4cf23cb@narada> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 22:00 28/02/99 +1100, narada wrote: >Thanks Morgan >Before I abandon the virtual fractal field model completely ... >(snip) >>All that's defined of the virtual particles surrounding a real particle is >>the probability that the virtual particles might be there. Since the >>virtual particles only "might be" there in the cloud, for the probabality >>distribution to have any more structure than a smooth blur there has to be >>some reason for the virtual particles to favour possibly being in one part >>of the cloud more than in another. > > >Hmm. Perhaps the source from which I took my visualisation was taking too >many metaphorical liberties, however, I'm sure I remember that virtual >particles (clouds, raindrops?) can have their own virtual particles, and so >on indefinitely, the only proviso being that the probabilities diminish >toward infintesimal at an enormous (but finite) speed. And also that all >interactions between "real particles" begin as the exchange of virtual >particles. True they only exist at a particular location with a certain >degree of probability and it is hard to see how they would favour one >location over another except in regard to distance from their source. > By no means am I demanding you give up your visualisation! The book would have to have _something_ to draw! Remember that it's only a visualisation (an artist's impression, if you will) - and don't forget that virtual particles are always paired with their antiparticles (to keep the books balanced) and are no smaller than their real counterparts, so don't forget to have plenty of room available for the less likely appearances (hydrogen atoms, uranium nuclei, Mercedes SLKs, atom-for-atom duplicates of yourself...) My favourite fractal visualisation is to use the Lyapunov types of Fractint to represent the surface of the universe at those really tiny scales, thirty-five powers of ten deep, where the very concept of spacetime dissolves into froth - the streaks across the surfaces representing paths of light (ie. straight lines). Naturally, they are only artists impressions - the details have no physical significance, they are far simpler than the real thing is supposed to be, and they lack at least two or three dimensions. >>Obviously, I'm referring to the _net_ energy of the Universe. It can >>shuffle debits and credits around internally as much as it likes, it would >>still be an unobservable virtual particle by the standards of an external >>observer. > >So you are admiting that this exnihilo universe at least is entierly virtual >in its nature unless one is inside and a part of the system? > Well, from the outside there's nothing to observe. Even a black hole has more features. If interactions did take place (and an interaction of _some_ sort would be necessary to measure anything), then we aren't even looking at the whole universe. Of course, the observable universe may not be everything (inflationary models, in fact, insist that the Observable Universe (everything within (Age of Universe)*2 light-years of here) is only a miniscule fraction of the whole thing. >I still find visualising subatomic particles (and their interactions) as >fluctuations of probability within fractaline fields intuitively satisfying. >Within the present model AIUI(as I understand it) one of the annoying >problems is that one cannot predict when something will happen, only the >likelyhood of its happening at a given time. This was what Einstien objected >to in his famous quote about God not choosing playing dice with the >universe. So why does the electron emit a photon and change energy states at >this moment rather than that moment? > It's not impossible - one of the things assumed in QM is that electrons are indistinguishable - so when an electron sets out from a source and arrives at a target one is in no position to ask if it's the same electron or another electron (just like it). Maybe there was a sort of a daisy chain of virtual electrons surrounding virtual electrons surrounding ... with the source and target electrons being the endpoints of the chain (in fact, in some formalisations this is exactly what goes on). Virtual particles can certainly become real. The most impressive case of this is in the immediate vicinity of black holes. A pair of virtual particles (they always get created in pairs - the particle and its antiparticle) are created in the immediate vicinity of a black hole's event horizon. One crosses the event horizon and is lost, and the other manages to escape. Et voila, a real (anti)particle has apparently emerged from the black hole - and indeed, measuring the black hole's statistics (mass, angular momentum, and electric charge), one finds them changed by exactly the same amounts as would account for those properties of the new particle. An alternative equivalent interpretation is that a particle within the black hole managed to briefly travel faster than light, and so escaped from the hole. There's no violation of relativity, because one can never catch the particle in the act (since one cannot observe virtual particles). You just look that way and find it already there, looking very pleased with itself. In short, virtual particles cannot be measured, unless their accompanying antiparticles are eliminated. Since this can only happen when said antiparticle meets a real particle of the appropriate type, no overall change has occured. --->TIME---> ---- e- ---->--------\ *-->photon /->- e+ ->-/ photon-->* \->- e- ->--------> (Which could just as equally be interpreted as an electron briefly travelling backwards in time; with photons either actually kicking the electron into making the detour, or being generated by the electron in a manner analogous to an optic boom (Cerenkov radiation)). But who know what's going on inside the things? Well, not literally "inside" in the case of electrons, since they're supposed to have minimal radius (on the order of the Planck length). One of the most intriguing suggestions is that of Roger Penrose. The system evolves along all possible histories (the many-worlds hypothesis) until a certain threshold is reached and the system has "spread out" a certain distance among the space of possibilities. Note that this threshold isn't a simple spatial one that would be measured in terms of how far apart the possible locations of a given particle are - that could be light-years. Penrose suggests something along the lines of "when the difference in the gravitational fields of the alternate configurations are different enough (if you subtracted one from the other and measured the energy of the highest peak remaining), then a collapse occurs." There's all sorts of variations on this theme, of course - plenty to keep people interested testing. I can see a potentially fractal structure looming here. The system could easily develop a fractal distribution among the space of possible states, by following a suitably chaotic dynamic (imagine a quantum pinball machine). Now imagine how different thresholds may prune this system back so that it appears classical on larger scales. Different parts of the system may diverge faster than other parts, and so collapse sooner; then would start spreading out again under the influence of Schrodinger's equation. Depending on the size of the threshold, the system as a whole may collapse in its entirety, or large sections collapse, leaving small pockets of uncertainty, or (as in the case of classical pinball machines) the threshold can be so low that the divergences and collapses are undetectable. In fact, now that I come to think of it, this sounds like Andre Linde's model of the Big Bang, called "chaotic inflation". Morgan L. Owens _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 3 07:42:00 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id GAA29163 for philofractal-list; Wed, 3 Mar 1999 06:42:03 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from blue.hermes.net.au (blue.hermes.net.au [203.35.8.194]) by rock.icd.com (8.9.1/8.9.1) with SMTP id GAA29108 for ; Wed, 3 Mar 1999 06:28:24 -0600 Received: from narada (unverified [203.35.207.150]) by blue.hermes.net.au (EMWAC SMTPRS 0.83) with SMTP id ; Wed, 03 Mar 1999 23:28:07 +1100 Message-ID: <003e01be6573$8399ed20$96cf23cb@narada> From: "narada" To: Subject: Re: [philofractal] Musings on narada's musings Date: Wed, 3 Mar 1999 23:42:49 +1100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.2106.4 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.2106.4 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Thanks Jim for so quickly answering my musing about 4D fractals with your FOTD. I'll check it out! Best Wishes All Ways N _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 3 07:42:01 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id GAA29167 for philofractal-list; Wed, 3 Mar 1999 06:42:08 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from blue.hermes.net.au (blue.hermes.net.au [203.35.8.194]) by rock.icd.com (8.9.1/8.9.1) with SMTP id GAA29104 for ; Wed, 3 Mar 1999 06:28:19 -0600 Received: from narada (unverified [203.35.207.150]) by blue.hermes.net.au (EMWAC SMTPRS 0.83) with SMTP id ; Wed, 03 Mar 1999 23:28:05 +1100 Message-ID: <003d01be6573$81dde540$96cf23cb@narada> From: "narada" To: Subject: Re: [philofractal] Musings about metaphors, modelling, etc Date: Wed, 3 Mar 1999 23:40:27 +1100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.2106.4 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.2106.4 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com (snip) >By no means am I demanding you give up your visualisation! The book would >have to have _something_ to draw! Remember that it's only a visualisation >(an artist's impression, if you will) - and don't forget that virtual >particles are always paired with their antiparticles (to keep the books >balanced) and are no smaller than their real counterparts, so don't forget >to have plenty of room available for the less likely appearances (hydrogen >atoms, uranium nuclei, Mercedes SLKs, atom-for-atom duplicates of yourself...) LOL. (snip) >>I still find visualising subatomic particles (and their interactions) as >>fluctuations of probability within fractaline fields intuitively satisfying. >>Within the present model AIUI(as I understand it) one of the annoying >>problems is that one cannot predict when something will happen, only the >>likelyhood of its happening at a given time. This was what Einstien objected >>to in his famous quote about God not choosing playing dice with the >>universe. So why does the electron emit a photon and change energy states at >>this moment rather than that moment? >> >It's not impossible - one of the things assumed in QM is that electrons are >indistinguishable - so when an electron sets out from a source and arrives >at a target one is in no position to ask if it's the same electron or >another electron (just like it). Maybe there was a sort of a daisy chain of >virtual electrons surrounding virtual electrons surrounding ... with the >source and target electrons being the endpoints of the chain (in fact, in >some formalisations this is exactly what goes on). > (snip) >One of the most intriguing suggestions is that of Roger Penrose. The system >evolves along all possible histories (the many-worlds hypothesis) until a >certain threshold is reached and the system has "spread out" a certain >distance among the space of possibilities. Note that this threshold isn't a >simple spatial one that would be measured in terms of how far apart the >possible locations of a given particle are - that could be light-years. >Penrose suggests something along the lines of "when the difference in the >gravitational fields of the alternate configurations are different enough >(if you subtracted one from the other and measured the energy of the >highest peak remaining), then a collapse occurs." There's all sorts of >variations on this theme, of course - plenty to keep people interested >testing. > >I can see a potentially fractal structure looming here. The system could >easily develop a fractal distribution among the space of possible states, >by following a suitably chaotic dynamic (imagine a quantum pinball >machine). Now imagine how different thresholds may prune this system back >so that it appears classical on larger scales. Different parts of the >system may diverge faster than other parts, and so collapse sooner; then >would start spreading out again under the influence of Schrodinger's >equation. Depending on the size of the threshold, the system as a whole may >collapse in its entirety, or large sections collapse, leaving small pockets >of uncertainty, or (as in the case of classical pinball machines) the >threshold can be so low that the divergences and collapses are undetectable. > >In fact, now that I come to think of it, this sounds like Andre Linde's >model of the Big Bang, called "chaotic inflation". Ah, now this is a much more concise and technically correct analogy for the patterns I was conceptualising. I shall need to ponder this for a while... Best Wishes All Ways N _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 3 07:42:01 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id GAA29171 for philofractal-list; Wed, 3 Mar 1999 06:42:09 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from blue.hermes.net.au (blue.hermes.net.au [203.35.8.194]) by rock.icd.com (8.9.1/8.9.1) with SMTP id GAA29102 for ; Wed, 3 Mar 1999 06:28:13 -0600 Received: from narada (unverified [203.35.207.150]) by blue.hermes.net.au (EMWAC SMTPRS 0.83) with SMTP id ; Wed, 03 Mar 1999 23:28:02 +1100 Message-ID: <003c01be6573$7fbd2820$96cf23cb@narada> From: "narada" To: Subject: Re: [philofractal] Musings on four questions - possibly irrelevant aside. Date: Wed, 3 Mar 1999 23:30:52 +1100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.2106.4 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.2106.4 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com >>You know the funny thing about religions, (and I have tried a few of them), >>is that they all have a reason why they dont consider themselves to be in >>the class of 'religion'. Basically they all think they have the TRUTH, and >>that the other systems are lacking in this that or the other. "Scientific >>Materialism" is I believe the dominant religion on this planet at this time. >>It has infiltrated and subsumed most previous religions, and is so >>universally accepted that most of its adherents are unaware that it is a >>belief system, let alone a religion! They simply believe that they are >>studying the TRUTH. >> >They believe they are studying _reality_ - Science makes no official claims >as to the _truth_ of its ideas. And if what they're studying is not >reality, they'd like to know what the hell is. "Reality is merely an illusion, albiet a very persistant one". Albert Einstien But seriously, I think truth (even in capitals) pretty much implies 'about reality' as a subject, and in this context 'truth' and 'reality' are nearly synonymous. Let me rephrase in case that helps- They simply believe they are studying reality. Within its own parameters I would say that science certainly does make claims as to the truth of its ideas, both implied ones and 'official' ones. Just because the disclaimer is added that they are theoretical or mathematical models doesnt change the reality that they are generally accepted by the flock (and the priests) as higher knowledge, and given the emotional and psychic importance that others reserve for more traditional religious belief systems. >Science doesn't offer absolutes; sorry. If you want those you'll have to go >elsewhere. > >And Mathematics doesn't offer truth either; sorry. Alfred Tarski >mathematically proved as much in 1933. Many religions offer less absolutes than the religion of scientific materialism does. Dont make the mistake of thinking that the dogmas of popularised Christianity constitute religion. Any religion worthy of the name contains much profound reflection upon the nature of everything. Religious thought can be as subtle and concise and original as scientific logic is, (and also as capable of self deception). The scope of religious thought however is far greater than scientific thought as it includes the whole of our emotional mental spiritual natures as well as the physical. It is also more humane in that it attempts to answer questions more important to human beings than science does, such as, how we can be truly happy, or what constitutes wisdom and maturity. >>I do appreciate that some of the voices here have travelled the path of >>scientific materialism a considerable distance, and have gleaned much wisdom >>and insight into the nature of their own reality >> >Which would have to be the same as everyone else's, otherwise we're not >talking about reality. Mmm. There were a few ambiguities in that phrase "nature of their own reality" weren't there. ;-) So if 'reality' is what you cant escape, what makes you think that we are all trapped in the same trap? Im not saying that science doesnt study a universally shared reality, but I see no proof that it does. I find that one of the reasons I relate to so many people easily is that I am prepared to accept that what is true for me may not be true for them. Part of the information overload that society is going through at the moment seems to be that only with the widom of hindsight will we ever be able to say get an overview of what was really important. (and even that will be biased). Witness the number of scientific FACTS that are not hotly disputed by someone on the web! Is this not another of the doctrines of scientific materialism that "WE are studying the ONE TRUE REALITY, and thats what makes our religion so much better that its not really a religion at all"!? >> Also, is 'shape' a relative phenomena in the sense that something is curved >>only in referance to another part of itself? Normally one thinks that if >space >>becomes 'curved' enough it reaches its limit when it turns 360 degrees and >>closes on itself spherically, but what if space were curved like a fractal >>spiral? What if it curved in x many dimensions but remained 'open' in others? >> >Ah, now there you're getting into metric topology, where curvature becomes >irrelevant to defining the object - a field of mathematics which happens to >include much of the study of fractals within it! Oh goodie, now I have a name for it I can look it up on the web. Thanks. (seriously). I have noticed in learning many things, mechanics and computer skills in particular, that the path to becoming an expert consists mostly in knowing the right names for things. :-) Best Wishes All Ways N _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 3 19:42:17 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id SAA00417 for philofractal-list; Wed, 3 Mar 1999 18:42:07 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp0.mindspring.com (smtp0.mindspring.com [207.69.200.30]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id SAA00282 for ; Wed, 3 Mar 1999 18:12:10 -0600 Received: from LOCALNAME (user-2iveh9l.dialup.mindspring.com [165.247.69.53]) by smtp0.mindspring.com (8.8.5/8.8.5) with SMTP id TAA10597 for ; Wed, 3 Mar 1999 19:13:24 -0500 (EST) Date: Wed, 3 Mar 1999 19:13:24 -0500 (EST) Message-Id: <1.5.4.16.19990303191214.337f9e86@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] Re: Musings on narada's musings Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 10:12 PM 3/3/99 +1300, Morgan wrote: At 13:30 02/03/99 -0500, Jim wrote: >>Don't feel heretical if you find some pseudoscience >>interesting and not easily cast aside. As I wrote in my most >>recent FOTD, the pseudoscience of one century can become the >>true science of the next century. > >But don't go claiming that it's scientific _yet_. If you're >going to do that you might as well try entering a jetboat in >the next America's Cup - because the Cup rules might be changed >to allow jetboats in the future. I make no claims that any of the current pseudoscientific fads are scientific. Quite the contrary, by definition they are not scientific, and most certainly they cannot be scientifically demonstrated. But I wish that skeptics would not assume *all* paranormal phenomena to be false, merely because *some* are false. I also wish that skeptics and Atheists would not use science to attempt to disprove the mystical things of religion. Remember that a negative cannot be proven. The most that can be done is to make a paranormal or mystical explanation seem less likely by presenting a rational explanation for an unexplained event that is more likely. >They [scientists] believe they are studying _reality_ -- >Science makes no official claims as to the _truth_ of its >ideas. And if what they're studying is not reality, they'd like >to know what the hell it is. Maybe they're studying a mental model -- a particular state of consciousness, the contents of which for purposes of convience has been given the name "physical universe", and also given an arbitrary attribute known as reality. But isn't it incredible that after all this scientific enlightenment, we still cannot agree on what reality means? (I have no one but Einstein, Bohr, Everett, etc. to blame for this borderline mystical view of the world.) >And Mathematics doesn't offer truth either; sorry. Alfred >Tarski mathematically proved as much in 1933. Almost a circular argument here -- proving with math that math doesn't offer truth! But interesting. ;-) Jim Muth jamth@mindspring.com _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Thu Mar 4 01:42:06 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA02233 for philofractal-list; Thu, 4 Mar 1999 00:43:14 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp1.mindspring.com (smtp1.mindspring.com [207.69.200.31]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA02162 for ; Thu, 4 Mar 1999 00:28:34 -0600 Received: from LOCALNAME (user-2iveiiu.dialup.mindspring.com [165.247.74.94]) by smtp1.mindspring.com (8.8.5/8.8.5) with SMTP id BAA08189 for ; Thu, 4 Mar 1999 01:29:44 -0500 (EST) Date: Thu, 4 Mar 1999 01:29:44 -0500 (EST) Message-Id: <1.5.4.16.19990304012917.0d27f590@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 04-03-99 (Halfway to Julia) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 04. 1999 Fractal enthusiasts: Today was warm and breezy here at Fractal Central, but a heavy thunder-storm in the early evening kept it from being perfect. The temperature of 65F 18C, however, was perfect for hunting fractals. For the hunt, I packed my supplies and sallied forth once again into the wilderness of the Z^2+C Julibrot, journeying this time into the impenetrable tangle of the negative spike. (I refer to it as a spike, because the more familiar term has fallen from favor.) What is the actual shape of the negative spike of the Mandelbrot set? When only the M-set itself is considered, the spike is a straight line, studded with an infinity of midgets, which extends to C=-2. But the M-set is only a single slice through the center of the 4-D Julibrot, so what is the shape of the entire 4-D spike? To begin, it is not simply a one-dimensional spike, but rather an intricate matrix of three-dimensional spaces, curved in the four- dimensional space. In 4-space, a 2-space cuts a 3-space in a 1-space. In everyday language, in four-dimensional space, a plane cuts through a three-dimensional space in a line. The negative spike of the M-set is the line where the plane of the screen cuts through the 3-space of the Julibrot matrix. The spike is straight because the 3-space happens to be flat at that particular point. In other orientations, the spike breaks down completely, appearing as curved lines, which are actually curved 3-spaces. Once again, we are limited by our inability to visualize spaces of more than three dimensions. When I try to picture a curved 3-space, I invariably find myself picturing a curved plane with some thickness. This is not at all like a three-space, which can have the shape of a cube, yet can be curved in 4-D space, and joined along its opposite faces into a hypercylinder without stretching or wrinkling. The actual spike complex consists of curved 3-spaces, with shafts and sheets shooting off in several unimaginable directions to infinity. The entire spike complex is impossible to describe, but the three-dimensional cross- sections are interesting. Today's fractal is also interesting. It is a picture of a midget on the negative spike, located in the East Valley area of the prominent midget at -1.75. It is not a baby Mandelbrot set, for it is sliced in the same halfway-to-the-Julia direction as yesterday's FOTD. But even when viewed from this odd direction, it retains most of its Mandelbrot characteristics. The most obvious difference is the totally alien pattern of features surrounding the central midget. The curly t-shaped objects around the edge are familiar enough from M- and J-views in the East Valley areas of midgets, but the stretched, almost tortured effect closer to the midget has no comparison in the classic M-set or the J-sets. I named the picture "Halfway to Julia" because that's where it is. The parameter file draws in a minute or two, or if you'd rather not calculate it, the GIF file can be retrieved already calculated from Usenet at: and from Paul's web site at: Get there quick if you want to beat the crowd. As for me, I'm going to stay right here at Fractal Central, and continue cranking out those glorious fractals. The next one will appear in 24 hours. Until then, take care, and don't discard your fractals before they're worn out. Jim Muth jamth@mindspring.com START FORMULA============================================= multirot-XY-ZW {; draws 6 planes and many rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(z)+c, |z| <= 36 } END FORMULA=============================================== START PARAMETER FILE====================================== Halfway_to_Julia { ; 3min on a 486-100, 640x480 reset=1960 type=formula formulafile=multirot.frm formulaname=multirot-XY-ZW function=ident/flip center-mag=-2.46825530754099100/0/697273.8 params=-45/45/0/0/0/0 float=y maxiter=7200 bailout=25 inside=0 logmap=93 symmetry=xaxis periodicity=10 colors=000LEJ<7>4J5<10>`JpcJthGy<7>NXxKZxJbw<18>8Bx\ <23>iJ_<21>9xrZruwlx<3>cdYDSr_cSzn1<12>7s8<15>jKU<4>\ rZ_sa`wNTz9LW_H2zD<19>315<5>cT2<7>DaW<17>\ sZg<10>YiuWjvVky<14>MkdQIfMkc<15>7TATfXntr<9>eQ` } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Halfway_to_Julia { ; 3min on a 486-100, 640x480 reset=1960 type=formula formulafile=multirot.frm formulaname=multirot-XY-ZW function=ident/flip center-mag=-2.46825530754099100/0/697273.8 params=-45/45/0/0/0/0 float=y maxiter=7200 bailout=25 inside=0 logmap=93 symmetry=xaxis periodicity=10 colors=000LEJ<7>4J5<10>`JpcJthGy<7>NXxKZxJbw<18>8Bx\ <23>iJ_<21>9xrZruwlx<3>cdYDSr_cSzn1<12>7s8<15>jKU<4>\ rZ_sa`wNTz9LW_H2zD<19>315<5>cT2<7>DaW<17>\ sZg<10>YiuWjvVky<14>MkdQIfMkc<15>7TATfXntr<9>eQ` } frm:multirot-XY-ZW {; draws 6 planes and many rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(z)+c, |z| <= 36 } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Thu Mar 4 19:42:06 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id SAA07446 for philofractal-list; Thu, 4 Mar 1999 18:42:08 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id RAA07248 for ; Thu, 4 Mar 1999 17:57:12 -0600 Received: from packrat.nznet.gen.nz (ms2-24.nznet.gen.nz [203.167.232.154]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id MAA09845 for ; Fri, 5 Mar 1999 12:57:36 +1300 Message-Id: <3.0.3.32.19990304213811.006deb94@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Thu, 04 Mar 1999 21:38:11 +1300 To: philofractal@icd.com From: "Morgan L. Owens" Subject: Re: [philofractal] Re: Musings on narada's musings In-Reply-To: <1.5.4.16.19990303191214.337f9e86@pop.mindspring.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 19:13 03/03/99 -0500, Jim wrote: >At 10:12 PM 3/3/99 +1300, Morgan wrote: > >>But don't go claiming that it's scientific _yet_. If you're >>going to do that you might as well try entering a jetboat in >>the next America's Cup - because the Cup rules might be changed >>to allow jetboats in the future. > >I make no claims that any of the current pseudoscientific fads >are scientific. Quite the contrary, by definition they are not >scientific, and most certainly they cannot be scientifically >demonstrated. But I wish that skeptics would not assume *all* >paranormal phenomena to be false, merely because *some* are >false. I also wish that skeptics and Atheists would not use >science to attempt to disprove the mystical things of religion. >Remember that a negative cannot be proven. The most that can >be done is to make a paranormal or mystical explanation seem >less likely by presenting a rational explanation for an >unexplained event that is more likely. > On this I concur completely. Die-hard atheists of my acquaintance tease me about leaving open the possibility of a Creator of the Universe. I've posted earlier on this list a possible scenario in which the entire Universe as we know it is a (not necessarily accurate) historical recreation of the dim distant past - ourselves included. It is an entirely unfalsifiable suggestion, and hence has no role to play in science. Science _can_ in many cases test specific claims held by religions about the Universe - the age (and shape) of the Earth, the origin of the diversity in human languages, and so on. It's here that skirmishes can occur. Science is also prepared to test its own claims (when funding is available). After all, it's _much_ more fun when a theory, especially a long-established one, fails than when it's a matter of "ho, hum, another spectacular confirmation". > >>They [scientists] believe they are studying _reality_ -- >>Science makes no official claims as to the _truth_ of its >>ideas. And if what they're studying is not reality, they'd like >>to know what the hell it is. > >Maybe they're studying a mental model -- a particular state of >consciousness, the contents of which for purposes of convience >has been given the name "physical universe", and also given an >arbitrary attribute known as reality. But isn't it incredible >that after all this scientific enlightenment, we still cannot >agree on what reality means? > But if it's just a mental model, then isn't it incredible that we can agree on so much? But it's okay; we can't even seem to agree on what a religion is :-) >>And Mathematics doesn't offer truth either; sorry. Alfred >>Tarski mathematically proved as much in 1933. > >Almost a circular argument here -- proving with math that math >doesn't offer truth! But interesting. ;-) > Oh, yes; not only is Mathematics a religion, but it's the only religion capable of proving itself to be one! :-) Morgan L. Owens _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Thu Mar 4 23:42:29 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id WAA08434 for philofractal-list; Thu, 4 Mar 1999 22:42:01 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from dot.crosswinds.net ([204.50.152.131]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id WAA08384 for ; Thu, 4 Mar 1999 22:27:54 -0600 Received: from default (170-112-111.ipt.aol.com [152.170.112.111]) by dot.crosswinds.net (8.8.7/8.8.8) with SMTP id XAA06712 for ; Thu, 4 Mar 1999 23:30:48 -0500 (EST) (envelope-from nleseul@zurich.crosswinds.net) Message-ID: <000d01be66c0$44e70f60$6f70aa98@default> From: "Nature Leseul" To: Subject: Re: [philofractal] Re: Musings on narada's musings Date: Thu, 4 Mar 1999 22:25:49 -0600 X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.3110.5 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.3110.3 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com <<>>And Mathematics doesn't offer truth either; sorry. Alfred >>Tarski mathematically proved as much in 1933. > >Almost a circular argument here -- proving with math that math >doesn't offer truth! But interesting. ;-) > Oh, yes; not only is Mathematics a religion, but it's the only religion capable of proving itself to be one! :-)>> If it can prove itself, doesn't that make it not a religion anymore? :-P I'd like to see that proof that mathematics is not truth, though. I mean, unless you can disprove one of the basic things like 1+1=2 or a=a, it seems pretty solid, and I don't know of any way to challenge the basic axioms. !i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i !i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i! i!i! Nature Leseul i!i! i!i! "I wil play you some Mozart, if you like, which wil onlyi!i! i!i! make you weep, but my Don Juan, Christine, burns, i!i! i!i! and yet he is not struck by fire from Heaven... You i!i! i!i! see, Christine, there is some music that is so terriblei!i! i!i! that it consumes all who approach it." i!i! !i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i !i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i!i! _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Fri Mar 5 00:42:24 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA08689 for philofractal-list; Thu, 4 Mar 1999 23:42:01 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from eagle.ACNS.ColoState.EDU (root@eagle.ACNS.ColoState.EDU [129.82.100.90]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA08672 for ; Thu, 4 Mar 1999 23:37:16 -0600 Received: from yuma.ACNS.ColoState.EDU (yuma.ACNS.ColoState.EDU [129.82.100.64]) by eagle.ACNS.ColoState.EDU (AIX4.3/UCB 8.8.8/8.8.8) with ESMTP id WAA53950 for ; Thu, 4 Mar 1999 22:38:11 -0700 Received: from holly.colostate.edu (res099037.HALLS.ColoState.EDU [129.82.99.37]) by yuma.ACNS.ColoState.EDU (AIX4.3/UCB 8.8.8/8.8.8) with ESMTP id WAA142998 for ; Thu, 4 Mar 1999 22:38:07 -0700 Message-ID: <36DF6DAE.D7D3B527@holly.colostate.edu> Date: Thu, 04 Mar 1999 22:37:50 -0700 From: Xylen X-Mailer: Mozilla 4.5 [en] (Win95; U) X-Accept-Language: en MIME-Version: 1.0 To: philofractal@icd.com Subject: Re: [philofractal] Re: Musings on narada's musings References: <000d01be66c0$44e70f60$6f70aa98@default> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Nature Leseul wrote: <> > I'd like to see that proof that mathematics is not truth, though. I mean, > unless you can disprove one of the basic things like 1+1=2 or a=a, it seems > pretty solid, and I don't know of any way to challenge the basic axioms. > I guess it all depends on what you call the basic axioms, and just what 'kind' of truth you are looking for. ;) I recently ran across a few interesting definitions about mathematicians, and their metaphysical beliefs. I thought this list would appreciate the definitions. Platonism A platonist believes that mathematical objects exist independent of the human mind, and a mathematical statement is objectively either true or false. Constructivism A constructivist believes that the only acceptable mathematical objects are ones that can be constructed by the human mind, and the only acceptable proofs are constructive proofs. Formalism A formalist believes that mathematics is strictly symbol manipulation and any consistent theory is reasonable to study. For a formalist the notion of truth is confined to the context of mathematical models, e.g., a formalist would say "The parallel postulate is false in Riemannian geometry." but she wouldn't say "The parallel postulate is false." I guess I probably fall into the Formalist category, but fractals don't seem to care what you believe in, they still exist. Perhaps that is the ultimate truth. Xylen -- ----------------------------------------------------------------------- "I've been placed on this world to accomplish a certain number of things. Right now I am so far behind, I will never die" http://members.tripod.com/~Xylen Fight Spam! Join CAUCE! == http://www.cauce.org/ ----------------------------------------------------------------------- _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Fri Mar 5 01:42:07 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA08908 for philofractal-list; Fri, 5 Mar 1999 00:42:01 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from camel8.mindspring.com (camel8.mindspring.com [207.69.200.58]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA08873 for ; Fri, 5 Mar 1999 00:31:31 -0600 Received: from LOCALNAME (user-2iveghq.dialup.mindspring.com [165.247.66.58]) by camel8.mindspring.com (8.8.5/8.8.5) with SMTP id BAA23798 for ; Fri, 5 Mar 1999 01:32:30 -0500 (EST) Date: Fri, 5 Mar 1999 01:32:30 -0500 (EST) Message-Id: <1.5.4.16.19990305013155.2ed730a6@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 05-03-99 (The Same Midget) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 05, 1999 Fractal enthusiasts: The day started with blowing and swirling snow, which accumulated to 3cm before being attacked by a brilliant sun. The temperature of 41F 5C melted the snow by late afternoon, and by nightfall, one could never guess it had snowed. In other words, it was a perfect day for hunting fractals. The fractal I found for today is a different view of the same midget that appeared in yesterday's picture. I have therefore named it "The Same Midget" It is and it is not a Minibrot; it is and it is not a hole in a Julia set. It is and it is not something entirely new. Mandelbrot midgets and Julia set holes are actually the same four-dimensional bubbles in the Julibrot, viewed from different directions. The two varieties can easily be distinguished by an experienced fractal explorer. But the Julibrot is four-dimen- sional, and there are many directions in which it may be sliced other than the Mandelbrot and Julia directions. Just as the Mandelbrot and Julia slices have their unique characteristics, so do the slices in these other directions, which I lump into the category of odd slices. The holes in many of the odd slices resemble Julia sets. Other odd slices contain Mandelbrot-shaped midgets. But some slices cut through the 4-D Julibrot bubbles in slices that resemble neither Mandelbrot nor Julia midgets. Today's picture, which is closest to the Rectangular direction, shows a fine example of one of these un-named midgets. It is obviously not a Mandelbrot midget, though viewed from a different direction it would be. Nor is it a Julia set, which it would be if viewed in the Julia direction. It is simply a hole in an oblique slice through the East Valley area of the C=-1.75 midget of the Z^2+C Julibrot. The characteristic T-shaped elements of the East Valley area are there, surrounding the object at the center, but that object itself is almost outrageously different. Gone are the artistic curves of the M- and J-sets. In their place is a tortured object with two straight edges and two edges that appear as though they had been torn violently from the fractal fabric itself. Yet this bizarre object is also a Mandelbrot midget, and a midget-hole Julia set, for, like so many things in the world around us, the correct definition depends upon the aspect being observed. The picture can be calculated in a few minutes from the parameter file, or downloaded in about the same time from the Usenet binary newsgroup: where it has been posted for several hours. It can also be picked up on the WWW at: Tomorrow is 24 hours away. I'll arrive at that time with a new fractal, perhaps a different aspect of today and yesterday's midget-hole, and a few words of discussion about who-knows- what. Until then, take care, and bow your head in respect when you speak the word 'fractal'. Jim Muth jamth@mindspring.com START FORMULA============================================= multirot-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p2, c=e*imag(pixel)+p3: z=sqr(z)+c, |z| <= 36 } END FORMULA=============================================== START PARAMETER FILE====================================== The_Same_Midget { ; 7-1/2min on a 486, 640x480 reset=1960 type=formula formulafile=jim.frm formulaname=multirot-xz-yw passes=1 center-mag=+0.00000000564437052/-0.00000003120122262\ /465247.9/1.8571/54.497/-17.757 params=91.6/-84.1/-1.74532006/0/-1.74532006/0 float=y maxiter=2000 bailout=25 inside=0 logmap=98 symmetry=none periodicity=10 colors=000N0O<7>U0V<6>tDp<3>oTlnXkmajlfifif<2>udmubo\ oXgeS_WNS<3>cJ9bG4<11>rcAseAvd1uc6<6>nx`<5>FYq9Tt1Ly\ <8>LlaNo_OhVPaQQVLISb8Pw<12>TVU<5>t3Q<7>rDWrEWsFV\ <13>yIK<10>FAMB9M53K<13>FeYFadFdhFlYGsL<4>FoQ3yK<7>m\ Mi<5>XtL<13>cKScHSbHR<14>e5Yc6X<11>y4d<3>z9ezAfzAf\ <13>zAmzAnzAozApzAq<7>zAyzAzzAzzAzzAz } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= The_Same_Midget { ; 7-1/2min on a 486, 640x480 reset=1960 type=formula formulafile=jim.frm formulaname=multirot-xz-yw passes=1 center-mag=+0.00000000564437052/-0.00000003120122262\ /465247.9/1.8571/54.497/-17.757 params=91.6/-84.1/-1.74532006/0/-1.74532006/0 float=y maxiter=2000 bailout=25 inside=0 logmap=98 symmetry=none periodicity=10 colors=000N0O<7>U0V<6>tDp<3>oTlnXkmajlfifif<2>udmubo\ oXgeS_WNS<3>cJ9bG4<11>rcAseAvd1uc6<6>nx`<5>FYq9Tt1Ly\ <8>LlaNo_OhVPaQQVLISb8Pw<12>TVU<5>t3Q<7>rDWrEWsFV\ <13>yIK<10>FAMB9M53K<13>FeYFadFdhFlYGsL<4>FoQ3yK<7>m\ Mi<5>XtL<13>cKScHSbHR<14>e5Yc6X<11>y4d<3>z9ezAfzAf\ <13>zAmzAnzAozApzAq<7>zAyzAzzAzzAzzAz } frm:multirot-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p2, c=e*imag(pixel)+p3: z=sqr(z)+c, |z| <= 36 } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Fri Mar 5 07:42:02 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id GAA10363 for philofractal-list; Fri, 5 Mar 1999 06:42:03 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from ns.krauch.com.py ([207.124.222.109]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id GAA10310 for ; Fri, 5 Mar 1999 06:25:23 -0600 Received: from Diosnel (router.krauch.com.py [207.124.222.118]) by ns.krauch.com.py (8.8.7/8.8.7) with SMTP id HAA15664 for ; Fri, 5 Mar 1999 07:33:09 -0400 Message-ID: <002f01be6768$2529aae0$4501010a@Diosnel.krauch.com.py> From: "Diosnel Herrnsdorf" To: Subject: RE: [philofractal] Re: Musings on narada's musings Date: Fri, 5 Mar 1999 20:27:40 -0400 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.3110.5 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.3110.3 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com ><<>>And Mathematics doesn't offer truth either; sorry. Alfred >>>Tarski mathematically proved as much in 1933. > I'd like to see that proof that mathematics is not truth, though. I mean, >unless you can disprove one of the basic things like 1+1=2 or a=a, it seems >pretty solid, and I don't know of any way to challenge the basic axioms. As far as I remember, the theorem just proved that there is no system that can prove itself to be completely self consistent. In other words, if you see the body from the inside, you can not see if it reaches to wrong conclusions. If my memory serves me right (which I doubt - it was long ago) the theorem means that, if you develop your system far enough from the basis, you will get some contradictions. I'll better let the ones who are in the theme explain it in a more mathematical way. Please note that I'm not neglecting math, it's just that I'm lead to other directions inside math. Regards, Diosnel _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Fri Mar 5 12:46:02 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id LAA11763 for philofractal-list; Fri, 5 Mar 1999 11:43:18 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp04.primenet.com (daemon@smtp04.primenet.com [206.165.6.134]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id KAA11440 for ; Fri, 5 Mar 1999 10:42:10 -0600 Received: (from daemon@localhost) by smtp04.primenet.com (8.8.8/8.8.8) id KAA18545 for ; Fri, 5 Mar 1999 10:17:15 -0700 (MST) Received: from usr06.primenet.com(206.165.6.206) via SMTP by smtp04.primenet.com, id smtpd018498; Fri Mar 5 10:17:12 1999 Date: Fri, 5 Mar 1999 09:42:50 -0700 (MST) From: Kerry Mitchell To: philofractal@icd.com Subject: RE: [philofractal] Re: Musings on narada's musings In-Reply-To: <002f01be6768$2529aae0$4501010a@Diosnel.krauch.com.py> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com On Fri, 5 Mar 1999, Diosnel Herrnsdorf wrote: > As far as I remember, the theorem just proved that there is no system that > can prove itself to be completely self consistent. In other words, if you > see the body from the inside, you can not see if it reaches to wrong > conclusions. I believe that was Godel's theorem, after Kurt Godel. He proved that any logical system strong enough to include arithemetic was unable to prove itself consistent. That means that there will always be true statements ("true" in the logical sense) that cannot be proven in the system. > If my memory serves me right (which I doubt - it was long ago) the theorem > means that, if you develop your system far enough from the basis, you will > get some contradictions. I don't think you'll necessarily get contradictions, but you won't be able to prove everything. As far as math not being "truth", perhaps that's because we don't know that the axioms of math ar the axioms of reality. Math is a logical system; the universe seems to be, but we don't know for sure. Without that knowledge, it seems to me the best we can do is exploit the fortuitious coincidences and not get carried away by the math when reality tells us something different. > Regards, > > Diosnel ------------------------------------------------------------------------------- Kerry Mitchell lkmitch@primenet.com http://www.primenet.com/~lkmitch/ ------------------------------------------------------------------------------- _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Fri Mar 5 21:42:08 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id UAA14718 for philofractal-list; Fri, 5 Mar 1999 20:42:18 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id TAA14515 for ; Fri, 5 Mar 1999 19:54:22 -0600 Received: from packrat.nznet.gen.nz (ms2-51.nznet.gen.nz [203.167.232.181]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id OAA26788 for ; Sat, 6 Mar 1999 14:54:26 +1300 Message-Id: <3.0.3.32.19990306145232.006e5314@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Sat, 06 Mar 1999 14:52:32 +1300 To: philofractal@icd.com From: "Morgan L. Owens" Subject: RE: [philofractal] Re: Musings on narada's musings In-Reply-To: <002f01be6768$2529aae0$4501010a@Diosnel.krauch.com.py> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 20:27 05/03/99 -0400, you wrote: >><<>>And Mathematics doesn't offer truth either; sorry. Alfred >>>>Tarski mathematically proved as much in 1933. > > >> I'd like to see that proof that mathematics is not truth, though. I mean, >>unless you can disprove one of the basic things like 1+1=2 or a=a, it seems >>pretty solid, and I don't know of any way to challenge the basic axioms. > > >As far as I remember, the theorem just proved that there is no system that >can prove itself to be completely self consistent. In other words, if you >see the body from the inside, you can not see if it reaches to wrong >conclusions. > >If my memory serves me right (which I doubt - it was long ago) the theorem >means that, if you develop your system far enough from the basis, you will >get some contradictions. > Godel showed that any sufficiently powerful formal system (basically, one that can be used to do arithmetic) is either (a) inconsistent, in which case all statements and their negations can be proved in the system, or (b), in which case there as statements that, although true, cannot be proved. In his paper "On Formally Undecidable Propositions of Principia Mathematica and Related Systems", Godel constructed a statement which said, in effect, "This statement cannot be proven in the system of Principia Mathematica". If the system is consistent, then obviously the statement cannot be proven. Conversely, if the statement is proven, then the system cannot be consistent. He later showed how other formal systems necessarily have either flaw (a) or flaw (b), and is not restricted to the particular axiomatisation of mathematics that forms the Principia Mathematica. At this stage, we are in a position to say that either mathematics is consistent, or it is not. To prove it is inconsistent, all we need to do is find a statement F for which we can prove both F and not-F. With a suitable chain of reasoning, F could be any statement, like "1+1=2", but an inconsistency would more likely be first discovered in more esoteric domains. If it is consistent, we never prove the fact. But even if mathematics is consistent and we can't prove all true statements, we should at least be able to feel confident that all statements we prove are true. Tarski says no. Tarski built a formal system which was provably consistent (it was too simple to qualify for Godel's Theorem to apply). In this system he defined a property Q for which he could prove the following statements: Not all positive integers have property Q. 1 has property Q. 2 has property Q. 3 has property Q. ... Where the list goes on for all positive integers. At least one of this infinite list of statements must be false, because to take them all together would yield an inconsistency. But which one? It's no good trying to look at each one individually - they can all be proven. It's no good taking them in pairs, or triples, or ... any finite selection (or even most infinite ones), since any such selection will be consistent. The power of Godel's Theorem comes from the fact that "sufficiently powerful" systems of mathematics are able to describle themselves - Godel used the system of Principia Mathematica to prove things about the incompleteness of Principia Mathematica. Tarski used Principia Mathematica (or equivalent system) to prove things about the artificial formal system in which he constructed his attack on truth. Whether such a situation can occur in Principia Mathematica itself (or whatever sufficiently powerful formalisation of mathematics you use) can never be known - not without proving and comparing simultaneously an infinite number of statements. Morgan L. Owens _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Sat Mar 6 01:42:06 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA15664 for philofractal-list; Sat, 6 Mar 1999 00:42:01 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp1.mindspring.com (smtp1.mindspring.com [207.69.200.31]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA15630 for ; Sat, 6 Mar 1999 00:31:45 -0600 Received: from LOCALNAME (user-2iveijh.dialup.mindspring.com [165.247.74.113]) by smtp1.mindspring.com (8.8.5/8.8.5) with SMTP id BAA27256 for ; Sat, 6 Mar 1999 01:32:13 -0500 (EST) Date: Sat, 6 Mar 1999 01:32:13 -0500 (EST) Message-Id: <1.5.4.16.19990306013135.297f313a@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 06-03-99 (The Eyes Have It) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 06, 1999 Fractal enthusiasts: Today was sunny and chilly here at Fractal Place. The temperature of 46F 8C was perfect enough, but due to an unexpected load of work, I had little time to search for fractals. But I made the most of the limited time by breaking out a new formula and finding a quickie fractal. The new formula, named "O-varesc" is the same as the old formula named Oblate, but with a variable escape radius added as real(p3). Using this new formula, I have caught a picture in the Oblate direction of the Seahorse Valley area of a tiny midget on the negative tail, just as it is about to be swallowed by the ever- decreasing cut-off point. The parameter file takes 18 minutes to run on a high-speed 486. The GIF file takes about one minute to download from: <>alt.binaries.pictures.fractals or from: I'd better wrap it up at this point, as the screen is beginning to look snowy -- a sure sign I'm ready to fall asleep. Until next time, take care, and once you escape beyond the escape radius, you'll never return. Jim Muth jamth@mindspring.com START FORMULA============================================= O-varesc {; Jim Muth real(z),imag(c) a=sqr(p3), z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| < a } END FORMULA=============================================== START PARAMETER FILE====================================== The_Eyes_Have_It { ; 18min on a 486-100, 640x480 reset=1960 type=formula formulafile=varesc.frm formulaname=O-varesc passes=1 center-mag=0/0/2.629774e+007/0.0001948/-0.004/-89.978 params=0/0/-1.6234513150326/0/1.623452/0 float=y maxiter=18000 bailout=25 inside=0 logmap=103 symmetry=xyaxis periodicity=10 colors=000Kaq<12>rOQ<4>iVN<21>HSRYEIm1AecX<5>ZU9c`Dg\ fGklJ<6>zRN<8>jNy<2>kZziQ3<2>EPvDYi<19>XAiV7q<3>fENi\ GFj2LlH8<3>YlP<7>fsGktG<8>Hs8AqA<6>az1<8>OI7ND8K77\ <13>kRAmSApS5<10>gbo<5>eQPOGZeOLyX6<18>ZD_<15>zgF<5>\ IOC<5>wyL<13>fYVW8GeXVrxl<4>`mXMbi<2>Kao } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= The_Eyes_Have_It { ; 18min on a 486-100, 640x480 reset=1960 type=formula formulafile=varesc.frm formulaname=O-varesc passes=1 center-mag=0/0/2.629774e+007/0.0001948/-0.004/-89.978 params=0/0/-1.6234513150326/0/1.623452/0 float=y maxiter=18000 bailout=25 inside=0 logmap=103 symmetry=xyaxis periodicity=10 colors=000Kaq<12>rOQ<4>iVN<21>HSRYEIm1AecX<5>ZU9c`Dg\ fGklJ<6>zRN<8>jNy<2>kZziQ3<2>EPvDYi<19>XAiV7q<3>fENi\ GFj2LlH8<3>YlP<7>fsGktG<8>Hs8AqA<6>az1<8>OI7ND8K77\ <13>kRAmSApS5<10>gbo<5>eQPOGZeOLyX6<18>ZD_<15>zgF<5>\ IOC<5>wyL<13>fYVW8GeXVrxl<4>`mXMbi<2>Kao } frm:O-varesc {; Jim Muth real(z),imag(c) a=sqr(p3), z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| < a } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Sun Mar 7 01:42:02 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA21715 for philofractal-list; Sun, 7 Mar 1999 00:42:13 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp2.mindspring.com (smtp2.mindspring.com [207.69.200.32]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA21612 for ; Sun, 7 Mar 1999 00:18:04 -0600 Received: from LOCALNAME (user-2iveidu.dialup.mindspring.com [165.247.73.190]) by smtp2.mindspring.com (8.8.5/8.8.5) with SMTP id BAA14708 for ; Sun, 7 Mar 1999 01:18:19 -0500 (EST) Date: Sun, 7 Mar 1999 01:18:19 -0500 (EST) Message-Id: <1.5.4.16.19990307011731.0aef2db2@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 06-03-99 (Ouch---Let Me Go) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 07, 1999 Fractal enthusiasts: Today was one of those changeable days, which brought sleet, followed by rain, followed by a sunny warm afternoon, followed by more rain in the evening and high winds at night. All this plus a temperature of 55F 13C made it a perfect day for churning out fractals. As one might guess, I churned. To find today's fractal, I went to a point quite deep in the East Valley of the prominent minibrot at C=-1.75 of the Z^2+C Mandelbrot. To see the midget itself, go to the Mandel formula and draw a fractal with the center at -1.749977684531109 and a magnitude of 2.25e+009. Set the maxiter to at least 6000 and the Log Palette to 0. Notice the nice circular pattern around the midget. But today's picture has not been given a name such as "Fancy Midget". It has been named "Ouch---Let Me Go". And this is because in the direction of today's slice, the pattern around the midget is pulled, stretched and distorted as though unseen hands were trying to tear it apart. The scene really does slice directly through the midget, which lurks at the center. But due to the extreme distortion, it is not recognizable. What is the true four-dimensional shape of an object that in one direction appears as a minibrot, in another direction as a circle, and in an in-between direction as today's abomination? I have not the slighest idea, nor do I have the ability to visualize the entire thing, though I can say that it is a matrix of four-dimensional shapes, twisting through hyperspace. Even a 4-D person could not see the entire midget, for it lies in the interior of a hypersolid 4-D object. Such a person could see only the surface volume of the entire Julibrot, which would be interesting enough though. A being would need five-dimen- sional vision to see all the interior detail of the 4-D Julibrot in the manner we see the detail in the interior of a 2-D slice. But the 4-D person would have the advantage of seeing the interior of 3-D slices of the Julibrot. Having only three dimensions to work with, I must content myself with visualizing the interiors of only 2-D slices of the Julibrot. But those slices are endless and endlessly rewarding, and they are nothing but numbers. This leads me to the question: what are numbers? But that's a story for another day -- perhaps tomorrow. For today, the GIF file has been posted to: and to the WWW at: I see it's time to close down the fractal shoppe, feed the cats, and settle down to doze off watching a junky old sci-fi film. Check here again tomorrow, when I'll return with another fractal and a bit of philosophy. Until then, take good care, and how would one weigh a fractal? Jim Muth jamth@mindspring.com START FORMULA============================================= multirot-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p2, c=e*imag(pixel)+p3: z=sqr(z)+c, |z| <= 36 } END FORMULA=============================================== START PARAMETER FILE====================================== Ouch---Let_Me_Go { ; 16min on a 486-100, 640x480 reset=1960 type=formula formulafile=multirot.frm formulaname=multirot-XZ-YW passes=1 center-mag=+0.00000051798071517/-0.00000000131028874\ /2.812561e+008/2.886e-005/0.024/89.975 params=-46.6\ /-46.1/-1.74997768450147/0/-1.74997768450147/0 float=y maxiter=5000 bailout=25 inside=0 symmetry=none periodicity=10 colors=000mbZmebJDP<7>eM7<13>NW5<11>P2IP0JO1M<13>KFo\ _ZSor4giE_`NJHzK3zCBw43v<13>r`H<12>xuYxsZsqX<10>38I\ <8>VU`TFcR1eNqq<5>f1d<9>_MM<3>Ia6<15>he`moTrxL<4>LTN\ LTI<3>mLTgaRaqP<15>JWu<13>tp6<2>rVY<9>1FY<8>5U1<2>TO\ S<15>DFA<11>f8rh8uiAr<4>kHhoXSn_V } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Ouch---Let_Me_Go { ; 16min on a 486-100, 640x480 reset=1960 type=formula formulafile=multirot.frm formulaname=multirot-XZ-YW passes=1 center-mag=+0.00000051798071517/-0.00000000131028874\ /2.812561e+008/2.886e-005/0.024/89.975 params=-46.6\ /-46.1/-1.74997768450147/0/-1.74997768450147/0 float=y maxiter=5000 bailout=25 inside=0 symmetry=none periodicity=10 colors=000mbZmebJDP<7>eM7<13>NW5<11>P2IP0JO1M<13>KFo\ _ZSor4giE_`NJHzK3zCBw43v<13>r`H<12>xuYxsZsqX<10>38I\ <8>VU`TFcR1eNqq<5>f1d<9>_MM<3>Ia6<15>he`moTrxL<4>LTN\ LTI<3>mLTgaRaqP<15>JWu<13>tp6<2>rVY<9>1FY<8>5U1<2>TO\ S<15>DFA<11>f8rh8uiAr<4>kHhoXSn_V } frm:multirot-XZ-YW {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p2, c=e*imag(pixel)+p3: z=sqr(z)+c, |z| <= 36 } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Mon Mar 8 01:42:00 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA28080 for philofractal-list; Mon, 8 Mar 1999 00:42:01 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from camel7.mindspring.com (camel7.mindspring.com [207.69.200.57]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA27992 for ; Mon, 8 Mar 1999 00:19:33 -0600 Received: from LOCALNAME (user-2iveiil.dialup.mindspring.com [165.247.74.85]) by camel7.mindspring.com (8.8.5/8.8.5) with SMTP id BAA16017 for ; Mon, 8 Mar 1999 01:19:24 -0500 (EST) Date: Mon, 8 Mar 1999 01:19:24 -0500 (EST) Message-Id: <1.5.4.16.19990308011834.298f44bc@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 08-03-99 (A Fractal Conch) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 08, 1999 Fractal enthusiasts: Today was sunny, but very windy and cold here at the Fractal Central. With a temperature of 25F -4C, it was a perfect day for investigating the world of fractals. The formula I chose to investigate is the first of my HyperBrot series. This formula, which calculates with four-part hypercomplex numbers, draws two-dimensional slices through an eight-dimen- sional Julibrot object. In this unimaginable hyper-object, the true Mandelbrot set is four-dimensional, while the four-dimen- sional Julia sets comprise an eight-dimensional whole. Four dimensions are hard enough to imagine; eight-dimensions are beyond consideration. But a few things can be said about an 8-D object. Through any point there are eight mutually perpendicu- lar lines, 28 mutually perpendicular two-dimensional slices, and 56 mutually perpendicular three-dimensional slices. It's too bad that I have no idea how to write formulas to really investi- gate the unimaginable slices of this beast, but my hyperbrot formulas make a rudimentary attempt in this direction. I have named today's picture "A Fractal Conch" because as I studied it, searching for a name, the thought of a conch shell came into my mind. The picture shows a hole in the hyper- Mandelbrot set, which was discovered almost by accident when I entered a maxiter of 75,000 instead of 7,500. Like most of my fractals, today's picture is to be considered an adventure in fractal land rather than a work of art. Real art cannot be produced in a production-line manner. The parameter file runs very slowly for several reasons. First, the extreme maxiter is necessary to reveal the detail inside the hole; second, the periodicity checking must be turned off, or nothing at all appears; finally, the passes should be set to 1 so as not to miss any small detail. On the fastest 486, calcula- tion will take 4 hours, so downloading the GIF file from the usual sources is highly recommended. Although the image is a Mandelbrot fractal, it has many charac- teristics of a Julia fractal, though without the usual Julia symmetry. The GIF file has been posted to Usenet at: and to Paul's web site at: <>http://home.att.net/~Paul.N.Lee/FotD/FotD.html Once again I failed to get to my intended bout of philosophy, but tomorrow is another day and another fractal, and if all goes well, some philosophical ramblings. So look for me then. Until that time, take care, and long live the great fractal. Jim Muth jamth@mindspring.com START FORMULA============================================= HyperBrotI {; Jim Muth a=p1, b=0,0, d=real(p2), h=imag(p2), f=p3: g=sqr(a)-sqr(b)+pixel, b=d*a*b+f, a=h*g, |a|+|b| <= 9 } END FORMULA=============================================== START PARAMETER FILE====================================== A_Fractal_Conch { ; 4hrs on a 486-100, 640x480 reset=1960 type=formula formulafile=hyprbrot.frm formulaname=HyperBrotI passes=1 center-mag=+0.14040845488529820/+0.00000136213711807\ /4.774252e+008/1/22.499 params=0/0/10/1/9.9999999999\ 99999e-021/0 float=y maxiter=75000 bailout=25 inside=0 logmap=566 symmetry=none periodicity=0 colors=000OZoZ`uP_qKapGalDaiC`iCZiAXhAWhAUh8Sd8Rc6P`\ 6OZ6MX5JU5HS3GP3DO3CM5DO6GP8HS8JUAKWCMZCO`DPbGRdGShH\ UkJWnKXqKZtMZuO`wObyPczRdzRfzShzUizWkzWlzXnzZpzZqz`r\ zbtzbtzcqzdnzflzhizhhzidzkczl`zlXznWzpSzqRzqOzrMztJz\ uGzuDzwAzy8zz5zz0zz3zy6zwAzt8zuDzuHzuKzwPzwSzwWzw`zy\ czyfwyktynqzqlztizyfzzbzzZzzWzzR<4>zz8Zzb3qz5pz6nz6n\ z8lz8lzAkzAizCizChzDhzDfzGfzHdzHczJczJbzKbzK`zMZzMZz\ OXzOXzPWzPWzOZzO`zObzOcz<2>OhzOizOlzOnz<4>OuzOwzMzyM\ zwMztMzrMzqMzpMzl<2>MzhMzfMzc<2>MzZMzXOzc<3>OyuOtzOp\ z<6>OHzfJzyJzzJqzJczHf<7>zGz<6>zGzwDzuDztDzqDzpDzlDz\ kDziDzkGzlHznHzpJzqJzrKztKzuMzwMzyOzzPzzPzzRzzRzzSzz\ SzzUzzUzzWzzXzzXzzZzzZzz`zz`zzbzzXzzbzzdz\ <6>zzz<19>zzz } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= A_Fractal_Conch { ; 4hrs on a 486-100, 640x480 reset=1960 type=formula formulafile=hyprbrot.frm formulaname=HyperBrotI passes=1 center-mag=+0.14040845488529820/+0.00000136213711807\ /4.774252e+008/1/22.499 params=0/0/10/1/9.9999999999\ 99999e-021/0 float=y maxiter=75000 bailout=25 inside=0 logmap=566 symmetry=none periodicity=0 colors=000OZoZ`uP_qKapGalDaiC`iCZiAXhAWhAUh8Sd8Rc6P`\ 6OZ6MX5JU5HS3GP3DO3CM5DO6GP8HS8JUAKWCMZCO`DPbGRdGShH\ UkJWnKXqKZtMZuO`wObyPczRdzRfzShzUizWkzWlzXnzZpzZqz`r\ zbtzbtzcqzdnzflzhizhhzidzkczl`zlXznWzpSzqRzqOzrMztJz\ uGzuDzwAzy8zz5zz0zz3zy6zwAzt8zuDzuHzuKzwPzwSzwWzw`zy\ czyfwyktynqzqlztizyfzzbzzZzzWzzR<4>zz8Zzb3qz5pz6nz6n\ z8lz8lzAkzAizCizChzDhzDfzGfzHdzHczJczJbzKbzK`zMZzMZz\ OXzOXzPWzPWzOZzO`zObzOcz<2>OhzOizOlzOnz<4>OuzOwzMzyM\ zwMztMzrMzqMzpMzl<2>MzhMzfMzc<2>MzZMzXOzc<3>OyuOtzOp\ z<6>OHzfJzyJzzJqzJczHf<7>zGz<6>zGzwDzuDztDzqDzpDzlDz\ kDziDzkGzlHznHzpJzqJzrKztKzuMzwMzyOzzPzzPzzRzzRzzSzz\ SzzUzzUzzWzzXzzXzzZzzZzz`zz`zzbzzXzzbzzdz\ <6>zzz<19>zzz } frm:HyperBrotI {; Jim Muth a=p1, b=0,0, d=real(p2), h=imag(p2), f=p3: g=sqr(a)-sqr(b)+pixel, b=d*a*b+f, a=h*g, |a|+|b| <= 9 } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue Mar 9 01:42:06 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA01883 for philofractal-list; Tue, 9 Mar 1999 00:42:02 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp5.mindspring.com (smtp5.mindspring.com [207.69.200.82]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA01670 for ; Mon, 8 Mar 1999 23:43:48 -0600 Received: from LOCALNAME (user-2iveh1f.dialup.mindspring.com [165.247.68.47]) by smtp5.mindspring.com (8.8.5/8.8.5) with SMTP id AAA16755 for ; Tue, 9 Mar 1999 00:43:08 -0500 (EST) Date: Tue, 9 Mar 1999 00:43:08 -0500 (EST) Message-Id: <1.5.4.16.19990309004208.298f695e@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 09-03-99 (What is this Fractal?) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 09, 1999 Fractal enthusiasts: It was another bright sunny but cold day here at the fractal enclave. The temperature of 30F -1C was perfect -- for hunting fractals that is. But before tackling today's fractal, I must tell of a dream I had this morning. Sometimes I have what are known as lucid dreams. This morning was the most recent. These are dreams in which for some reason my waking awareness returns but the dream does not end. When this happens to me, maybe once or twice a month, I am fully aware that I am dreaming, and I usually begin carefully observing the dream world around me. On occasion, the dream is so vivid that I must check to be sure I am dreaming. A sure way to check is to look for a large oak tree that was cut down 18 years ago to make room for a neighbor's driveway. In the dream world, this tree still stands, growing right through the asphalt of the driveway, but slowly dying as the years pass. It is a most curious world, this dream world, based as it is upon the physical world, but with different laws and strange inconsistencies. One of the more unusual features of this world of dreams is that within it, fractals can exist as real three- dimensional objects. I have come upon them lying about in odd places, and even hanging in mid-air. But try as I might, I have yet to see any object in this dream world that even remotely resembles a four-dimensional figure. The most striking thing when I find myself awake in this dream world is the realization that it consists of a vast collection of symbols that exists inside my mind, yet my mind, (or brain if you will), which is creating the world, is absolutely nowhere to be found in the dream. My mind is so much a part of the dream universe that it totally escapes observation. When I return to the physical world from this dream state, I sometimes wonder if the world we call the real world could be nothing more than a collection of symbols being visualized in the mind of some higher entity existing in some unimaginable higher world, and that higher world could itself be only symbols in the mind of a yet higher being . . . This sort of regression could go on forever. So I'll leave it to the reader to give a name to the highest of the higher entities. Now that the fractosophy is out of the way, it's time to notice the fractal. I have named the picture "What is this Fractal?". It's an image of a fairly mundane Julia set, with a two brilliant shafts slicing through the center. The Julia set, which appears as the dull red banded outer shape, is that of the Seahorse Valley area of the M-set. The two brilliant white shafts are part of Seahorse Valley itself, expanded to gigantic size. How is this possible? The answer involves a feature of four-dimensional geometry, which I have no time to explain this evening, but will explain thoroughly in tomorrow's FOTD. The unusual coloring effect is a result of combining the ranges and banding features of Fractint with one of my minimalist palettes. The parameter file runs in a few minutes, but for even faster viewing, the GIF file may be downloaded from: and from: I'll arrive tomorrow at this same time with another fractal and an attempt to explain the fourth dimension. Until then, take care, and may the fickle fractal of fate smile on your endeavor. Jim Muth jamth@mindspring.com START FORMULA============================================= multirot-XY-ZW {; draws 6 planes and many rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(z)+c, |z| <= 36 } END FORMULA=============================================== START PARAMETER FILE====================================== WhatIsThis_Fractal { ; 10min on a 486-100, 640x480 reset=1960 type=formula formulafile=jim.frm formulaname=multirot-XY-ZW function=ident/flip passes=1 center-mag=-0.915617/6.66134e-016/2.005519 params=86.5/86.5/0/0/-0.7/0 float=y maxiter=32767 bailout=25 inside=253 logmap=yes symmetry=xaxis periodicity=10 ranges=0/-1/100/102/105/109/115/125\ /135/150/175/225/32767 colors=000A00`PZZRlcVmhZnmb\ ordpsfqtjsumuxtxzzz000<238>000CCK000000 } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= WhatIsThis_Fractal { ; 10min on a 486-100, 640x480 reset=1960 type=formula formulafile=jim.frm formulaname=multirot-XY-ZW function=ident/flip passes=1 center-mag=-0.915617/6.66134e-016/2.005519 params=86.5/86.5/0/0/-0.7/0 float=y maxiter=32767 bailout=25 inside=253 logmap=yes symmetry=xaxis periodicity=10 ranges=0/-1/100/102/105/109/115/125\ /135/150/175/225/32767 colors=000A00`PZZRlcVmhZnmb\ ordpsfqtjsumuxtxzzz000<238>000CCK000000 } frm:multirot-XY-ZW {; draws 6 planes and many rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=sqr(z)+c, |z| <= 36 } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 10 02:15:07 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id BAA05048 for philofractal-list; Wed, 10 Mar 1999 01:15:02 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from blue.hermes.net.au (blue.hermes.net.au [203.35.8.194]) by rock.icd.com (8.9.1/8.9.1) with SMTP id AAA04861 for ; Wed, 10 Mar 1999 00:29:13 -0600 Received: from narada (unverified [203.35.207.161]) by blue.hermes.net.au (EMWAC SMTPRS 0.83) with SMTP id ; Wed, 10 Mar 1999 17:33:37 +1100 Message-ID: <000501be6ac2$39255460$a1cf23cb@narada> From: "narada" To: Subject: [philofractal] 4D Julias Date: Tue, 9 Mar 1999 19:51:36 +1100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.72.2106.4 X-MimeOLE: Produced By Microsoft MimeOLE V4.72.2106.4 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Jim Whilst finding your explanations and the recent FOTDs intriguing, I need some backgraound info to follow you properly. Can you reccomend a web page with something basic about the 4D structure of the Julia/Mandel? Best N _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed Mar 10 02:16:23 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id BAA05063 for philofractal-list; Wed, 10 Mar 1999 01:16:53 -0600 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from camel8.mindspring.com (camel8.mindspring.com [207.69.200.58]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA04928 for ; Wed, 10 Mar 1999 00:43:58 -0600 Received: from LOCALNAME (user-2iveigu.dialup.mindspring.com [165.247.74.30]) by camel8.mindspring.com (8.8.5/8.8.5) with SMTP id BAA11435 for ; Wed, 10 Mar 1999 01:50:50 -0500 (EST) Date: Wed, 10 Mar 1999 01:50:50 -0500 (EST) Message-Id: <1.5.4.16.19990310014943.2a0fa908@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 10-03-99 (Fractal Abacadabra) (c) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- March 10, 1999 Fractal enthusiasts: A light snow fell all day here at Fractal Central, accumulating about 4cm so far, with about another 2cm due overnight. The temperature of 24F -4.5C was perfect for hunting fractals. Yesterday's fractal was named "What is this Fractal". Actually, it was a picture of an almost-Julia set, with a grossly enlarged bit of Seahorse Valley stuck in the middle. But how can such a cut off fragment exist? Remember that the picture was an oblique slice through the four- dimensional Julibrot figure. Now imagine the shape of the familiar two-dimensional Mandelbrot set being painted on a 2-D pane of glass, somehow suspended in four-dimensional space. Imagine this image being illuminated by a beam of light coming from all the Julia directions on one side, and therefore casting a four-dimensional shadow in hyperspace. The shadow fades away into all the opposite Julia directions. Every ray of light in the semicircle of illumination will intersect the M-set at a right angle, and the shadow will therefore be in the shape of a nest of hypercylinders, a shape impossible to imagine, but a fairly simple figure of four dimensional space. Any 2-D slice through this shadow, parallel to the M-set, will find a perfect shadow of the M-set projected on it. This is what we get when we view perturbed M-sets. Now let's discard a dimension and think in the everyday world of 3-D. Picture an image of the painted-on-glass M-set cast onto a parallel sheet of paper by the sun. As long as the paper is parallel to the glass, the image will be a perfect replica of the M-set. But if the paper is at an angle to the glass, the projected image will be enlongated in one of its dimensions. If the paper is perpendicular to the glass, nothing but a series of parallel straight bands will be projected onto it. This is the cause of the straight-edged bridges in the odd planes of the Julibrot. This is as far as we can go in three dimensions, but in 4-D space, the paper can be further rotated, around its other axis, so that the projection of both axes of the M-set are enlongated. When both rotations are equal, every line in the paper is at the same angle to the glass. The result is an undistorted but enlarged image of the M-set projected onto the paper. If the double-rotation is one of 45 degrees, all linear dimensions of the original image are enlarged by a factor of 1.4142, and the area is doubled. Since yesterday's slice is double-rotated 86.5 degrees from the Mandelbrot direction, the image cast upon it is enlarged about 16 times in its linear dimensions, thus the overblown fragment of Seahorse valley is at 256 times its normal area. The effect of the valley sliding under the banded material is purely illusional, and is caused by the presence of low- iteration material cutting off the hypercylindrical Mandelbrot shadow figure, which exists only where its hypercylindrical shape is not obliterated by the low-iteration stuff of the Julibrot. The hypercylindrical shape is composed only of material of the highest iteration, whereas the low-iteration stuff is far more randomly arranged. Today's fractal is actually two pictures: "Fractal Abacadabra 1" and "Fractal Abacadabra 2". The first picture shows a perfectly normal Julia hole. The second picture shows what happens when this hole is double rotated only 1/4 of one degree from the Julia direction. Abacadabra! -- it is magically transformed into a minibrot. This minibrot is magnified about 230 times the size it appears in the Mandelbrot direction, which can be checked by setting p1 to 0,0. In the Julia version, the Mandelbrot shape has been enlarged to infinity, and all of it has