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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is based on the formula Z^(2.005)+(2*Z)+C. This formula produces a parent fractal which, on the surface, resembles the Mandelbrot set, but is entirely different inside. The main spike of this parent is infinitely divided instead of being a single infinitesimally thin filament as is the spike of the M-set. Today's image is located in the debris associated with this divided spike. I named the image "Powers and Dominions". The only reason I can give for the name is that the phrase came to mind when I noticed the heavenly blues surrounding the hellish reds. I am currently reading a book about the traditions of angels in various cultures, and these are two of the traditional nine orders of angels. But there is nothing angelic about the image, which rates only a 6. We have seen similar images simply too many times to rate today's any higher. At least the image is a fast one, finishing in only 1-1/4 minutes on the fast machine and 7 minutes on the slow unit. The pre-calculated image is available for instant viewing on the FOTD web site at: The morning fog cleared away by 9am leading to a perfect day here at Fractal Central on Sunday. The fractal cats enjoyed the temperature of 75F 24C, while I enjoyed having nothing to do. The next FOTD will be posted in 24 hours. Until then, take care, and fractals are every bit as real as the angels. Or it could be that angels are as real as fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
PowersAndDominions { ; time=0:01:15.85-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident passes=1
center-mag=-1.72115541311189900/+0.057607899272470\
40/6295098/1/-111.5/5.46746958873800537e-006 float=y
params=1/2.005/2/1/0/0/0/0 maxiter=1250 logmap=125
inside=0 periodicity=10
colors=000F09G07I07G0AF0DF0GD0JD1MC4PC8QABT9EX9H_7\
Ka7Nd6Qg6Si4Wl3_o3cr1eu1ix0mz0rz0pz3ny6lv9ksChoFfl\
IeiLdfOacQ__TYXXXT_UQaTOdRJgPGjLDmIApG7sD3vA0y90z7\
0z00z60zP0zU0zZ0zc0yh0vm0sr0px0mw0lu0ir1fo3cj4`g6Y\
d7Xa9T_AQXCOTDLPFMMFJOGGSGFVICZI9VJ7WJ4YL1hL0jM0kM\
0lO0cM0lO0kO0cP3iP6hP9gQCZQGeQJdSMcSPcSTcTXcT_cVcc\
VgcVkcXocXtaXxcYzhYzm`zmYzmVzmTzmQzmPzmMziLzeIzcGz\
cDzdCzd9zf7yf4xg3wg0vi0ui0tj0sj0rl0rl0rl0oi0mg0lf0\
jd0ic0ga0f`0dY0cX0aV0`T0_S0YQ0XP0VM0TL0SJ0QI0PG0OF\
0OA0MD0MG0LI0LL3LO7JPCJSGJVLIXPI_SIaXGc`GfdGiiFjmF\
mrFpvDrzDuzCxzDvzDvzDvyDvuDurDumDuiFudFu`FsYFsTFsP\
FsL4z0FsIPdf_QzdLzjFzpAyv4xz0zz0vp4sf9oYDlOJiDOd3S\
a0_Y0X_0V`1T`4Qa7PcCOcFMdIJfMIfPGgTFgXCi_Ajc9jh7km\
4mr6mv8owAqwEswJuwNwwSxwWyw_zzdzzizzmzzqzzwzzxzzyz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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=========================================
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times.
