; Date: Wed, 11 Dec 2002 09:16:12 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 11-12-02 (Spirals Without End [3]) ; Id: <1.5.4.16.20021211091830.0d972c32@pop.mindspring.com> ; --------- ; FOTD -- December 11, 2002 (Rating 3) ; ; Fractal visionaries and enthusiasts: ; ; Today's fractal might show actual new material in the hypercom- ; plex Mandelbrot set, or it might be an artifact of mathematical ; imprecision. But regardless of what it is, it's an image with ; spirals everywhere. There are single spirals, double spirals, ; even signs of triple spirals. In fact, the image is filled with ; spirals without end. And "Spirals Without End" is what I named ; it. ; ; The image is a zoom into a hidden valley that appears peeking ; between the converging straight arms of yesterday's "Hyperbud" ; image, where a new world appears to be only partly revealing ; itself. In contrast to yesterday's image, which suffered from ; resolution breakdown, today's image suffers from the near impos- ; sibility of finding an acceptable coloring. I finally settled ; on a very broad purplish palette, though the result still leaves ; much to be desired and drops the rating to a below-average 3. ; ; While fractaling, I sometimes wonder about the meaning of it ; all. Is the existence of fractals filled with a deep, as-yet- ; undiscovered meaning, perhaps about the nature of reality, or ; are fractals mere candy for the eyes? And what of the concept ; of meaning itself? Is it something invented by the highest ; known form of life on the planet Earth, or is the universe ; filled with it? Does meaning actually exist before a self-aware ; entity asks the question 'why'? Does meaning exist on a two- ; mile-wide chunk of ice orbiting in the cold loneliness of the ; Oort cloud, where observers never have and never shall venture ; to ask 'why'? ; ; And what of this fourth dimension with its hyper-objects? We ; can infer exactly how the various parts would fit together if it ; existed, but even knowing these things, we cannot visualize some- ; thing as simple as a tesseract. Does this mean that the fourth ; dimension does not exist? Does it mean that it does exist but ; we cannot visualize it? Does it mean that we have invented the ; whole puzzle as a mental exercise? Or does it mean anything at ; all? ; ; Don't expect answers any time soon. ; ; And don't expect an image soon if you try to run today's para- ; meter file. It takes 1-1/4 hours on my less-than-supersonic ; P-200 machine. The best way to see the puzzling image is to ; download it from Paul's web site at: ; ; ; ; or from Scott's site at: ; ; ; ; Tuesday's fractal weather was cloudy and chilly here at F.C., ; with a high temperature of 34F 1C. The ex-dynamic duo passed ; the unsatisfactory day lounging by the heat, except for when ; they were asking for food. ; ; This morning has brought freezing rain, which is even worse. ; It's a good day to remain indoors and get ahead on some work. ; Until tomorrow, when things will hopefully be more pleasant, ; take care, and try to make the best of bad situations as they ; arise. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ SpiralsWithoutEnd { ; time=1:15:40.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=1 center-mag=-0\ .04192332435179621/+0.08550882276013791/4021858 params=0/0/10/0/1e-014/0 float=y maxiter=20000 inside=255 logmap=-3100 periodicity=0 colors=0009ECAECBEDCEDDEDEEDFEDGGDHGFIGFJGFKGFLGFM\ GFNGHNGHMGHMGHMGHMGHMHHMHIKHIKHIKHIKHIKHIKHKIHKIHK\ IHKIHKIHKIHKKGMKGMKGMKGMKGNKGNMGNMGNMENMEPMEPMEPNE\ PNEPNERNERNDRNDRPDTPDTPDTPDTPDTPDVPDVRBVRBVRBVRBWR\ BWRBWTBWTBWTAYTAYTAYTAYVA_VA_VA_VA_V8_V8`V8`W8`W8`\ W8`W8bW8bW8bY6bY6dY6dY6dY6dY6d_6f_6f_4f_4f_4f_4g`4\ g`4g`4g`4g`4i`4i`4ib4ib4kb4kb4kb4kb4kd4md4md4md4md\ 4md4nf4nf4nf4nf4pf4pf4pf4pg4pg4rg4rg4rg4rg4ri4ti4t\ i4ti4vi4vi4xk4xk4yk4yk4zk4zk4zm4zm4zm4zm4zm4zm4zm4\ zn4zn4zn4zn4zn4zn4zp4zp4zp4zp4zp4zp4zr4zr4zr4zr4zr\ 4zr4zr4zt4zt4zt4zt4zt4zt4zv4zv4zv4zv4zv4zv4zx4zx4z\ x4zx4zx4zx4zy4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4\ zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx\ 4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4zx4z\ x4zx4zx6zx6zx6zx6zx6zx8zx8zx8zx8zxAzxAzxAzxAzxBzxB\ zxBzxBzxBzxDzxDzxDzxDzxEz } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } ; END PARAMETER FILE================================== ; ;