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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's splendid image owes its existence to the 'fmod' feature of Fractint, which creates the effect of overlapping bubbles. The parent fractal came about when I combined 100 parts of Z^(-3) with 1/100 part of Z^(2) and added C. With 10,000 times as much Z^(-3) as Z^(2), one would think the resulting fractal would be little more than the 4-pointed Z^(-3) Mandeloid, but actually it is a hugely enlarged Mandelbrot set, with bits of debris in the center of the main bay as well as in every bud. Today's image is located in an elephant trunk in the East Valley area of the parent. At first glance the central midget appears to be a routine one of this area, but a comparison with the same area of the true M-set will reveal that the pattern around the midget has changed. The change was enough to inspire me to a rating of an 8. The name "Test" was a total accident. I forgot to name the image, so I went with the default name of all parameter files created by the program. The calculation time of 1-1/4 minutes would be stretched to around 7 minutes on the slower computer. But regardless of the speed of the parameter file, it is always almost instantaneous to view the finished image on the FOTD web site at: Another perfect day (sunny, 73F 23C) went un-noticed here at Fractal Central on Tuesday. Of course, if the day was unnoticed, then how do I know it was perfect? That's a question worth pondering. The fractal cats pondered. They pondered their food dishes, that is. My day was routine in all respects, except for the fractal, which turned out better than I had hoped. The next fractal will appear in 24 hours. Until then, take care, and fractals are the strangest creatures ever. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Test { ; time=0:01:13.97-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident passes=1
center-mag=+27.7974630212/-0.7662145179/52524.91/1\
/-172.5/0 params=100/-3/0.01/2/0/350000/0/0 float=y
maxiter=1550 inside=0 proximity=500 periodicity=10
outside=fmod logmap=yes
colors=000wxwvwuuvstuqstorsmqrkpqiopgooenncmmalm_k\
lYkkWjjVijUhiUghTggSfgRefQdePddOcdObcNabM`aL_`KZ`J\
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88L78K69K59K49K39K29K19K09K1AK2AK3AK4AK5AK6AK7AK8A\
K9AKAAKBAKCAKDAKEAKFAKGAKHAKIAKJAKKAKKAKLAKMAKNAKO\
AKPAKQAKRAKSAKTAKUAKVAKWAKXAKYAKZAK_AK`AKaAKbAKcAK\
cAKdAKeAKfAPgAUhAZiAcjAhkAmlArmAvnAzoAzpAyqAyrAysA\
xtAxuAwvAwwAwzFwwAwuBwsBwqBwpBwnBwlBwkBriBmgBhfBcd\
BZbBUaBU_BVYBWWBWVBXTBYRBYQBZOB_MB_LB`JBaHBaGBaGB`\
HC`HC`HD_ID_IEZJEZJFZJFYKGYKGXLHXLHXLIWMIWMJVNJVNK\
VNKUOLUPLTQMTRMTRMURMUSMVSMVTMWTNXTNXTNYVNYWNZXN_Y\
N_YO`ZO`_Oa`Ob`ObaOcbOddNcbObaPa`Q`_R_ZSZYSYXTXWUW\
VVVUWUTWTSXSRYRQZQP_PO_OM`NLaMKbLJcKIdJHdIGeHFfGEg\
FDhEChDBiCAjB9kA8lB5nA7lSsBUtDVtFXtGYtI_tJ`tLbtMct\
OetPftRgtTitUjtWltXmtZot_ }
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.
