; Date: Thu, 13 Dec 2007 17:40:25 -0500 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 14-12-07 (The Whole Universe [No Rating]) ; ; Id: <1.5.4.16.20071213174223.2bd7ecb0@pop.mindspring.com> ; --------- ; ; FOTD -- December 14, 2007 (No Rating) ; ; Fractal visionaries and enthusiasts: ; ; Well, here it is in all its glory -- the parent fractal for the ; month of December -- the universe we have been exploring all ; this month. And what a world it is. To begin, its size is ; deceptive. The magnitude of an unusually small 0.0068 makes its ; area 10000 times the area covered by the Mandelbrot set. The ; center point of the image, -128,-30, is no mistake. We actually ; are this far from the origin. ; ; Studying the image, we notice that it is filled with rings, as ; have been most of the images so far this month. Every filament ; terminates in a decorative ring. Then we notice the main bay, ; if that's what it is. This nearly circular feature bears little ; resemblance to the cardioid shape of the classic Mandelbrot main ; bay. Where is East Valley, and where is Seahorse Valley? ; Actually, these features are in the fractal, though well hidden. ; ; We next notice the largest bud on this circular bay. Intuition ; says that it is the main bud, and would therefore have a periodi- ; city of 2. But actually, its periodicity is 13, as can easily ; be checked by counting the number of arms in its star. If there ; is a main bay in this parent fractal, it is very distorted. And ; look at the shape of the chaotic area leading from the large bud ; to the largest ring. It does rather resemble an East Valley ; elephant. ; ; The elephant resemblance is even more pronounced in the chaotic ; area of the slightly smaller bud north of the large one, which ; strangely enough has a periodicity of 12. It appears that ; nearly the entire shore line of the circular bay is the southern ; shore of the main bay of this fractal, and the farther we travel ; counter-clockwise, the deeper go into an East Valley environment. ; ; It is now simple to find the actual period-2 bud and Seahorse ; Valley. Simply count clockwise around the buds from the ; period-13 bud until the count reaches 2. There is our main bud, ; complete with Seahorse Valley and the main spike, all of them so ; small that a blow up is needed to make them visible at all. As ; we continue beyond the period-2 bud, the periodicity rapidly ; increases until we find ourselves deep in the north side of East ; Valley. ; ; This area of the fractal is actually the most interesting. The ; smaller circular bay just to the east is something entirely new. ; Nothing like it appears anywhere in the M-set. It is highly ; fragmented, and at first appears to be non-critical. But its ; shore is dotted with tiny irregular buds in which some very ; curious minibrots are well hidden. ; ; The fractal is also peculiar in that the orbits of the points ; diverge so fast as to be virtually invisible. Occasionally a ; single dot appears, but this is a rarity. Such rapidly ; diverging orbits are likely true of all fractals created with ; negative exponents of Z. ; ; I named the image "The Whole Universe", and so it is. I gave it ; no rating because I did virtually no work in producing it. But ; no one can complain about the calculation time of a superlumi- ; nal 28 seconds, which is about the time it will take to view the ; completed image on the FOTD web site at: ; ; ; ; Thursday was most unpleasant here at Fractal Central, as wet ; sloppy snow and cold rain fell most of the day, while the temper- ; ature hung just above freezing. The fractal cats spent the day ; by the heat, ignoring the weather. ; ; My day was uneventful. The next FOTD will be posted here in 24 ; hours. Until then, take care, and even though the concept of an ; ultimate reality might be a human invention, I really do believe ; in the virtual reality of fractals. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= The_Whole_Universe { ; time=0:00:28.17-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-128.674/-30.6294/0.006811989 params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 float=y maxiter=7500 inside=0 periodicity=10 colors=000tNitRgsLesUcsXbrW`rZZqYXq`VqZUpaSpZQo`Po\ YNnZLnXKmXImWHlWFmVDkVClUAkU9mU8lU7mU7lU6mU6lU5mU5\ lU4kU4lU3iU3iU4eU4eU4_U4aT4UT6YR7OR8SR9OPAPQBPNCRP\ DQNEROFQNHSNIRNJUMKSNLUMMTNNWMOUNPYMTUMV_MZbFddLek\ KmiMnsOvoTlo`bmfTklJirAlnIojPqfWtbcwZjyWqo`ifdbYiV\ PmOGrG7v9AsBDpDGnFJkHMiJTbQ_WWePalIgsBmy4sx5qx5ox5\ nx5lx5kx5ix5hx5fx5ew6cw6bw6`w6_w6Yw6Xw6Vw6Uw6Sw6Rx\ 7Sx7Tx7Ux7Vx7Wx7Wx8Xx8Yx8Zx8_x8`x8`x9ax9bx9cx9dx9e\ x9euBfsCgqDhoFilGjjHkhJkfKldLmaNn_OoYPpWRpUSqRTrPV\ sNTzLPqJKrLFjMmmOzjzzfzzbzz_zzWVzSXoPYqL_sH`tEasFb\ rFbqGcpGdoHdnHemIelIemHfnFfoDfoCdmBblB`kBZjBXiBVhA\ TgARfAPeAOdAPdBQdCRdDTdEUdFVdGXdIYdJZdK`dLadMbdOdd\ PedQfdRhdSidUjdVldWmdXLeuNfsPgrQhqSioUjnVkmXlkZmj_\ niaogcpfdqefrchsbitaku_mvZkwtlxplylmzhmzdnz`ZzU`zc\ bzmczrezvfzzhzzjzzkzzmzzVzzZzzazzdzzhzzkzzVzzWzzQz\ zSzzUzzYzzazzezzizzmzzpzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } ; END PARAMETER FILE========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint