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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is the last in the current series of seven Oblate pictures. (Well, all right, yesterday's image had more of a Rectangular orientation.) Today's image shows an Oblate view of a mini-Mandelbrot set lying in Seahorse Valley. The Mandelbrot version of the picture may be seen by changing the (p1) parameter from 0,90 to 45,45 and resetting the x-magnification factor to 1. When this is done, a perfectly-formed, though somewhat under-iterated, Mandelbrot midget typical of those in Seahorse Valley will appear. The pattern surrounding the Oblate midget closely resembles that of both the Mandelbrot and Julia versions of the scene. The main difference is that the pattern is distorted into a triangular shape. This triangular distortion is typical of most midgets in the Oblate orientation. The mathematical reason for this is probably known, though I have no idea of what that reason might be. The name "Seahorse Oblate" is a description, and hardly more than a catalog number. The rating of a 6 reflects the small amount of extra effort I put into the coloring. The render time of 3 minutes is about the same as the time required to go to the FOTD web site at: Starting with tomorrow's image, we will spend 7 days investigating what I call the Parabolic, real(c)real(z), orientation of the Julibrot. A sunny mild day on Sunday, with a temperature of 54F 12C, kept the fractal duo quite happy in the yard most of the afternoon. When evening came, they were so exhausted that they almost forgot their tuna. Today promises to be even warmer. This is good news for the dynamic cats. For me, there is a modicum of work to finish before I get to the fractals, the next of which will appear in 24 hours. Until then, take care, and sometimes I wonder whether there are an infinity of fractals or only one fractal with infinite aspects. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Seahorse_Oblate { ; time=0:03:06.09--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multirot-XY-ZW-new function=ident/flip
passes=1 center-mag=-0.00000000000200438/+0.000000\
00000203913/1.205523e+010/0.3459/32.5/3.8857805861\
8804789e-016 params=0/90/2/0/-0.7291299973892553/\
0.2357647081925723/-0.7291299973892533/0.235764708\
1925723 float=y maxiter=1800 inside=0
logmap=320 periodicity=10
colors=000jNvjNujNtiNsiNrhNqhNpgNogNnfNmfNleNkeOid\
PgdQecPcbOaaM_`LY_KWZJVZIT_KU`MUaOUbQWcSXcUZdW`eYb\
f_cgaehcfiehigijijkkllmmlnnmppnrqotspvtrxutzwvzxwz\
yzzzzzzzzzzzzPkWUkcYlaSm_NnYHoWCpU6qS1rQ8ZYEGeDFdC\
FcCEcBEbBDbADa9C`9C`8B_8B_7AZ7AZ6B`5Bb5Bd4Ce4Cg3Ci\
3Dj2Dl2Dn1Eo1Eq0Es0Et4Gs8IsBKsFLsINsMPsQQsTSsXUs_V\
sfbklicsqWyxOxuNxrNxoNwlMwjMwgMvdLvaLv_LuXKuUKuRPu\
OUzLZzNczRhzUlwYktalqdlnhlmlllolkjZjeMi`9dXE`UJXRO\
TNTOKYKHbGDgCAl87q9CrAGrBKrCPsDTsEXsF`sGetHitImtJq\
tKmpKjmKgjLdfLacLY`MVXMSUMPRMMOR`TWoY_zb`z``wZ`tYa\
qWanUakTahRbePbbOb_MbYLeWIhVGkUEmTCpSAsR8uQ6qO9nNB\
kLDhKFeJHbHJ_GLWFNTDPQCRNBTK9VH8XE7ZI6`L6aO6bS5cV5\
dY5f`5gd4hg4ij4jm4lq3mt3nw3oz3pr9rkEsdJtXPuQUvJZwK\
_rL`nMajNbfOcbPdZPdVSdUVdTYdT_bSa`ScZSdXSfVS8Hz8Jz\
9Lz9Nz9PzARzATzAVzOXz6Zz7`z7bz7cz8dz8ez8fz9fz9fz9f\
zAfzAfzAfzCfzEfzFfzHfzIfz }
frm:multirot-XY-ZW-new {; draws 6 planes and 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))+p3,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4:
z=z^(p2)+c,
|z| <= 36 }
END PARAMETER FILE=========================================
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times.
