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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I have pigeonholed the Mindspring connection problem for a while to devote my energies to the world of fractals, which is far less frustrating and far more fun. Today I investigated another 'evaporated' fractal, this time with a midget made visible by the fmod inside fill. The warhorse MandelbrotMix4 formula iterated the expression 4Z^(0.5)+0.04Z^(-3)+(1/C) to create a routine fractal featuring a routine Mandelbrot set. The routine nature of the fractal vanished when I raised the bailout radius to 1,000,000,000, which caused the entire fractal to evaporate, as all points became trapped. (The bailout has a great effect on formulae that contain negative powers of Z.) However, trapped points still do different things in their trapped condition, and Fractint's different inside fill routines can reveal interesting features, even when an image created with the normal flat equal-iteration bands and inside=0 will give nothing but a blank screen. To reveal the hidden detail in today's scene, I used the fmod inside fill, with the proximity set to 1.5. The result is an image with a totally unexpected series of sharp ridges, which reminds me somewhat of the pattern left in the sand by gently flowing water. Unable to find a better name, I named the image "FMOD Midget", and rated it a slightly liberal 7. With a render time of 15 minutes, the parameter file is a little slow. But in 16 hours relief will be available on the Usenet group: http://home.swbell.net/sdboyd56/fotd/ The fractal weather today was totally miserable as a combination of cold rain and snow fell all day. The wetness and temperature of 33F (0.5C) kept the fractal cats pinned to their favorite radiators most of the day. While working with today's fractal, I began wondering whether fractals are real or are created by fractal explorers in the act of fractal exploration. The question has been discussed before on the Philofractal list, but it's at least a sign that my long slumbering philosophical muse may be reawakening. If I can tear myself away from the connection problem long enough, I actually might be posting some worthwhile philosophy in a few days. For the moment, there's nothing to do but shut down the fractal shoppe and call it a night. Until next time, take care, and fractals are as real or unreal as one makes them, but as to whether they exist before being discovered, any opinion is as good as any other. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
FMOD_Midget { ; time=0:14:46.50 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-0.37795423333273510/+0.00011502762181923\
/1.141389e+009/1/47.499 params=100/0.5/1/-3/-0.96/10\
00000000 float=y maxiter=4800 inside=fmod
proximity=1.5 logmap=yes periodicity=10
colors=000OzzNzzNzzLzzLzzJzzJzzIzzIxzIvzGvzGuzEuzEsz\
DszDqzBqzBpzBpz9nz9nz8lz8lz6kz6kz4iz4gz4gz2fz2fz1dz1\
dz0bz0bz0`z0`z0_z0_z0Yz0Yz0Xz0Xz0Vz0Xz0Vz<2>0Vz0Vz0T\
z0Tz0Tz<2>2Tz2Sz4Sz6Sz6Sz8Sz9Qz9QzBQzDQzDQzEQzGOzGOz\
IOzIOzJOzLNzLNzNNzONzONzQNzRLzRLzTLzVLzVLzXJzYJzYJz_\
JzaJzaJzbIzdIzdIzfIzfIzgGziGziGzkGzlGzlGznEzpEzpEzqE\
zsEzsCztCzwCzwCzxCzzCz<3>zBzzBzzAzzAzzBzzCwwCtsEqnGp\
kGlfIkbJgYJfVLbQNaLNYIOXDQT9QR4SO1TN0TJ0VI0XE0_B0XD0\
VD0TE0SE0QG0OG0NI0JH0IH0GG0DH0AG08H06G05G05F<2>05H05\
H05J05J05L05L06N<2>07O08R08S09V09X1AY1A`2Aa4Ad4Ae6Ag\
6Ag8Ai8Ai9AkBAlBAlDAnDAnEApGApGAqIAqIAsJAsLAtLAwNAwN\
AxOAxQAzQAzRAzRAzTAzQAzTAz<3>_AzaAzbAzfAz<3>lBznBzpC\
zsCztLwtJxtIztEzwEzxGzzGzzIzzJtzLpzNk<2>zNXzNXzNYzNY\
zN_zN_zLazJazIbzGbzEdzLizSnxYssdxnkzkqzfxzazzXzzRzzR\
zzQzzQzzOzzOzz
}
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 20.0 PAR-FORMULA FILE==================================
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