|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: In the past I have several times been asked if I believe in miracles. The answer depends on the definition of the word 'miracle'. If a miracle is seen as a violation of natural laws brought about by the intervention of a supernatural deity, then I do not believe in miracles. True, many things take place that defy natural explanation, but these events are merely things that are not yet understood. They ultimately will be explained and then be seen to fit into the natural scheme of things, which will expand to include them. If a miracle is taken to be an event so unlikely as to be almost impossible, then yes, I do believe in miracles. People who desperately need money sometimes do win lotteries. A miracle of the latter variety appears in today's image. On the surface, the parent fractal of today's image is a Mandelbrot set. But the exponent of Z is 2.000001 instead of 2, which means it is not exactly a Mandelbrot set, but merely a very close approximation. One must search deep to find the tiny differences, but when they are found, they are so unexpected as to be a virtual miracle. Today's image lies deep in East Valley of the large midget on the main stem of the almost-M-set. It is so unlike anything in the true M-set that it must be considered a miracle, which is why I named it "The Miracle". The rating of a 9 may in fact be a bit conservative, but I am very hesitant about giving today's fractal a rating of 10, especially when I have not yet taken today's line of investigation to its limit, and do not yet know what I might find when I do. I could have used the manzpower formula to draw today's image, but that formula takes 12-1/2 minutes to finish the rendering. The MandelbrotN formula finishes in only 9 minutes, so this is the formula I used. Of course, rendering may be totally avoided by downloading the finished image from Paul's FOTD web site at: The fractal cats were happy on Monday when the sun shone and the temperature reached 72F 22C. This morning is starting cooler with a mixture of sun and clouds. Hopefully, the duo will be happy again. I'll be happy when the work is behind me. Until next FOTD, take care, and where will we go from here. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_Miracle { ; time=0:09:05.32--SF5 on a P200
reset=2004 type=formula formulafile=slices.frm
formulaname=MandelbrotN passes=1
center-mag=-1.74985154197874100/+0.000004742589482\
00/1.061936e+008/1/-162.5/-4.55138188755477291e-007
params=2.000001/0/0/0/0/0 float=y maxiter=2400
inside=0 logmap=325 periodicity=10
colors=000eKndKmcKlbKkaKj`Ki_KhZKgYKfXKeWKdVKcUKbT\
KaSK`RI_QGYO9WMFUKLS4Q31X06a0Af0Dl0Ip4Mu9PzDTzIXzM\
azJfsIllGpcDvXCzPAvLDsIFpFGlAJi7Lf4Mc1OX7JQDGLJCDP\
97V41`1CTAMOIXIP`LMcOJfQGjTDmXAp_9mf6jm4gs3dz1az0O\
fLAIc9Pf7Vg7`i6gj4ml4sm7v`AyODzAFz070zF0rL0jS0cY0V\
d0Oj0Gp09u0Jx0Tz0csAXmOPg`IaoAXz3Qz0`zAiyPrrazjpzc\
zfgoFl`PVP_DDi03c6CYFJSOQMVYGcdAll4us0zzIos`alsPfr\
LdpIdpFdoCdo9dUUUcccmmmzzzzzzzzzzzzzvzzszzpzzmxzju\
zgrzdoz_mzTmzOmxIlsClp6lm1lo0mo0op0pp0rr0sr0ur0uj3\
jcJaXYTSVSOSQJPPFMOCLOLIQTGS`DTiCVr9Xy7YoDQdJLXPDM\
V7C`03d0LzzCzg3zITdzOgzJjpFmc9oS4rF0u3MO0D_04j0_00\
T40PC0JL0FSOA_F4g70o0mXzf`r_ciTf`MiSFmI9p91s0Lr9Gs\
6Ds39u06u01v00v04_LlOG0Az0Qf0fGpSOa`FOg79o0Cgz3oTv\
Xmfc_QiLAp60zI0zD0z90z40y00y0VzOQzJMzFKzAPz7Uz3Zz0\
cz0hz6kz3nz1qz0tz0wz0zz0zzLzzFzzAzz6zz0zz0zzQzzQzz\
Qzz9zzZzzOzz7zzCzz9zz6zz3 }
frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16 }
END PARAMETER FILE=========================================
|
times.
