; Date: Sun, 25 May 2008 22:17:54 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 26-05-08 (The Fourth Dimension [Rating Arbitrary ; ]) ; ; Id: <1.5.4.16.20080525222103.2c1fc0a0@pop.mindspring.com> ; --------- ; ; FOTD -- May 26, 2008 (Rating Arbitrary) ; ; Fractal visionaries and enthusiasts: ; ; The unknown fascinates me, and what could be more unknowable ; than space of four dimensions? The problem is, while our math ; has no difficulty dealing with 4-D, and computers can be ; programmed to deal with it as logically as they do 3-D, we ; pathetic humans can do nothing more than twist our faces into a ; look of astonished puzzlement when asked to visualize something ; as simple as a 4-D tesseract. ; ; Today's image is a scene in Seahorse Valley of the Mandelbrot ; set, an object every tyro fractalist becomes familiar with the ; day after he discovers fractals. But the image bears little ; resemblance to either Seahorse Valley or its Julia set, yet what ; we are seeing is all part of the great Seahorse Valley complex. ; ; What has changed in the image is the angle at which we are ; viewing the valley. We are seeing it sliced at an angle very ; close to but not exactly in the Julia orientation. The Seahorse ; Valley Julia set (actually the -0.78,0 set) may be seen by ; changing the (p2) parameter to 0,0. The Mandelbrot aspect, ; which is Seahorse Valley itself, may be seen by changing the ; (p2) parameter to 1,0 and the (p4) parameter to -0.78,0. ; ; I can logically deduce what is going on in all these changing ; views of the same 4-D object, but I am no closer to visualizing ; the entire 4-D Seahorse Valley complex than I was that day 20 ; years or so ago, when I realized that the Julia sets and the ; perturbed Mandelbrot sets are differently oriented slices of a ; single 4-D object, the Julibrot figure. ; ; Perhaps what we call dimensions are simply another way of ; describing levels of consciousness, and mankind is now at the ; three-dimensional level of consciousness. This would imply that ; space appears three-dimensional because that is the only way we ; can perceive the abstract reality. If this is so, it is only to ; be expected that we would naturally develop a mathematics that ; would be compatible with and would confirm our perception. ; ; Enough philosophical rambling already. I named today's image ; "The Fourth Dimension" for obvious reasons. I gave it no ; rating, or rather left it to the individual viewer to decide its ; worth. ; ; The calculation time is but a few seconds, so have no fear when ; running the included parameter file. But if fear strikes, rush ; to the FOTD web site at: ; ; ; ; and view the finished image there. BTW, tomorrow's image will ; be a zoom into today's. ; ; Absolute perfection wrapped in a package -- that describes the ; conditions here at Fractal Central on Sunday. How can cloudless ; skies, low humidity, light winds and a temperature of 77F 25C be ; improved upon? ; ; The fractal cats must have agreed, for they sat in their window ; for an hour, watching me finish the yard work, while FL supplied ; encouragement and occasional refreshment. And despite all this ; activity, I still found time for the FOTD. The next FOTD will ; appear in 24 hours or so. Until then, take care, and seek total ; fulfillment in your endeavor. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= TheFourthDimension { ; time=0:00:14.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=EvenMoreSlices passes=1 maxiter=1800 center-mag=0/-0.0486/0.86 params=2/0/0/0.15/-0.78\ /0/0/0 float=y inside=0 logmap=yes periodicity=10 colors=000IJJ97P7DU6IY5Nb4Sf3Yj2bo1gs0lw6muCnsHoqN\ ooSpmUmkWjiYgg_deaaccZaeW_gTYiQWkNUmKSoHQpEOpBMmCK\ kEIhGGeIEbKC`MAYOBVQCSSDQTEPUDPVDOWDOXDNYDNZDM_DM`\ DLaCLbCKcCKdCJeCJfCIgCIhCHiBHjBGkBGlBFmBFnBEoBEpBG\ qEHrHJsJKtMLuONrNPpNRmNTkMUiMWfMYdL_aL`_LbYKdVKfTK\ gRJiOJkMJmJInHIoFIpCHqAHr8HpAIpBJoCJoDKoEKnFLmHLlI\ MlJMmKNmLOnMOoNPpPPqQQqRQqSRqTRqUSqVSoWTmXUkYViZWg\ _Xe`YcaZab__c`YcaWcbUccScdQceOcfMcgKchIciHcjHckHcl\ HcmHcnHcoHcpHcqHcrHcsHctHcuHcvHcwHcxHcyHczHczHczHc\ zHczHczHczHczHczHczHczHczHczHczHczHczHczHczHczHczH\ czHczHczHczHczHczHdzHezHfzHgzHizHkzHzzHzzHzzHzzHzz\ HyzHxzHzzIvzJuzKtzPszUrzZqzcozhmzmzzrzzvzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:EvenMoreSlices {; Jim Muth ; P1--exponent, P2--angle, ; P3--M center, P4--J center, z=pixel+(p4), c=p3+(pixel*p2): z=(-z)^(p1)+c, |z| < 16 } ; END PARAMETER FILE========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint