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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In today's modern world, there is simply too much information. No one can know everything about a single topic. One must specialize in a narrow area if they hope to break new ground, make new discoveries, become famous and perhaps rich. Except for the riches, the same is true of the field of fractals, which is infinite in an infinity of ways. For some reason, I became fascinated with midgets, (or atoms, minibrots, or molecules, as they are sometimes called), soon after I discovered the world of fractals. I did not do it intentionally. The world of fractals certainly extends far beyond midgets. But to me, a midget kind of defines the nature of the particular area of the particular fractal in which it lies. For example, today's image shows a midget in the fractal that results when portions of Z^(-1.6) and Z^(-8.5) are mixed and (1/C) is added. I named it "Many Ways to Go" because when searching for it, I had many opportunities to take a wrong turn, yet somehow found the right path to the midget. The scene has the typical nondescript appearance of scenes in inside-out fractals with negative exponents of Z. It is rather chaotic, the chaos mostly hiding the inevitable discontinuities. I have emphasized the different levels by varying the colors. But colors alone do not make a great fractal, and I could rate today's image no higher than average, which is a 5. To make matters worse, the render time is a dragging 29 minutes. But things can be made to go faster by downloading the finished image from the FOTD web site at: The temperature reached only 88F 31C here at Fractal Central on Thursday, but the humidity was very high, which made it feel worse than yesterday. The cats are not bothered by high humidity however, and chose to stay outside until a shower came up at 3pm, when they scampered for cover indoors. Despite having their day cut short, their moods were unexpectedly good. With the work pretty much up to date, my mood was good also. Today is starting cloudy and muggy. With the work still under control, I expect a similar day. The next FOTD will appear in 34 hours. Until then, take care, and what path would the sun describe in the sky of a four-dimensional planet? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Many_Ways_to_Go { ; time=0:28:43.01--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+1.61173239305630500/-0.154330402516033\
00/3.041086e+012/1/122.5/-0.0365804834360021272
params=-0.8/-1.6/-0.2/-8.5/-3/100 float=y
maxiter=3600 inside=0 logmap=560
periodicity=10 mathtolerance=0.05/1
colors=000hPugPufPuePtdPtcPtbPtaPs`Ps_PsZPsYPrXPrW\
PrVPrUPqUPqUPqUPqUPpTPpSPpQPpOPoNPoMPoLQoKSnJTnHVn\
FWnDYnBZn9`o7ao5co3dp1fp0gp0hp5eqCcrKarRZsZXteVt`X\
rXZqT`pObnKdmGflChk7ji3lh0ng0nf0me0id0gc1cb3aa4Za6\
W`7T_9QZANYBLYJMRzdLzaEzY8zV1zS0yP0wQ0uN0sM0qL0mK0\
iJ0eI0aH0YG0WF0UE0SD1QC1OB2NA2M93L83K73I64G54E45C3\
5A358F70Q80RB0RE0SG1SJ2SM3TO4TR4TT5UW6UZ7V`8Vc9VfA\
WhBWkBWmEYjH_hK`fNbdQdbTe`WgZZiWajUdlSgnQjoOmqMprK\
mmMjiNgePd`QbXR_TTXOUUKWRGXPCYUMTYVPacKelGU`NIPU6D\
`01g03h15i47j79jABkDDlGFlJHmMJnPLnSNoVPpYRp`TqcVrf\
Xzi_zlczohzimzcbiZbcTbZObTIlOCfI7rD1c70c22a18`0D_0\
JZ0OY0UX0_W0dV0jU0oT0kS5gREcQM_PVWObSNkPMsQOqQPpQR\
oQSnQUmQVlQWkQYiQZhQ`gQafQbeQddQecQgaQh`Qi_QkZQlYQ\
nXQoWQpVPoUOoTNoTMoSLoRKnRJnQInPHoPGpOFqNErNDsMCtL\
CuLFvNHwPKxRMyTOzURzWTzYVz_Yz`_zbazddzffzghzikzkmz\
mozndziVzeFzT0zH0za0zT1zL }
frm:MandelbrotMix4 {; 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,
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.
