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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I've been pondering some very important questions today -- questions such as: "are fractals alive?" and "if they are alive, are they animal, vegetable or mineral?" Common sense would dictate that fractals are neither animal, vegetable, nor mineral, but rather abstractions, and therefore cannot be considered alive. However, not being bound by common sense, I feel that the question remains open. Animals and vegetables are certainly alive. The behavior of certain mineral crystals comes close to life, and in certain occult disciplines minerals are considered to be the kingdom of life directly beneath the vegetable kingdom. Carrying this train of thought further, thinking humans are composed of molecules, molecules are composed of atoms, atoms are composed of sub-atomic particles, and sub-atomic particles appear to be composed of mathematical functions, which for convenience the human biological mind makes manifest to itself as particles. Fractals are also composed of mathematical functions, which the computer silicon mind makes manifest to the human senses as pretty pictures, fractal music, etc. Does this mean that fractals are alive in hyperspace? No, but it makes fractaling more interesting and gives skeptics something to explain away. Today's possibly living fractal is named "Mandelbrot Sylphs". A sylph is an elemental spirit of the air, a light airy thing, with gossamer wings and nothing to do but fly around heaven all day. Since I enjoy the firefly-like decorations on the filaments, which remind me of sylphs, I rated the picture a 7. The sylph formula is 500Z^(-2.49)-500Z^(-2.51)+(1/C), once again a whimsical creation. With a render time of just over 3 minutes, running the parameter file is the best way to see the sylphs fluttering against the deep astral blue of the sky. An alternate way to see the image is to wait 16 hours until it is posted to the Usenet group: The fractal weather today was sunny and cold. The temperature of 34F (1C) limited the fractal cats, who most certainly are alive, to 5 minutes on the porch and 10 seconds in the snow at the bottom of the porch stairs. My philosophical muse is coming back online, so the coming days could be interesting and enlightening. The next C-FOTD will appear in 24 hours. Until then, take care, and both fractals and people are ultimately composed of numbers, but what this means is anybody's guess. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Mandelbrot_Sylphs { ; time=0:03:08.12 -- SF5 on a p200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.0826770823005174/+0.448556725065169/98\
28077/1/-115 params=1/-2.49/-1/-2.51/449/11 float=y
maxiter=600 inside=0 logmap=50 periodicity=10
colors=00000F00F03G00H<4>00M00N00P<2>10Q10Q31Q31S43S\
43S64T64T76T76TCAXGD_JHaNKdSNgVSi_VlaYofarkdvniwrlzw\
ozztzzwzzzzzwzzvtzrkzpczoXzlNzkGzi9zf0zd0zc0UUQ03z3A\
z6Hz7Pz<2>EkzGpzHlzHiwHdvHarH_pHVnHSkHNiHKfHHdKMfMQg\
PTiQYkSalVdnXio_lp`pravtdxvfzwgzwlippNklQggTddXa`Y_Y\
`XTcTQfQMgPJkMEnJCpG7rD4vA0x70z60z40z40z9<2>0zK1zN1x\
S3wV3v_3va0o_0jX0fV0cS0cQ0cN0cK0cJ0cG0cE<3>0cC0cC0cC\
0dC0iA0nA0rA0w90z91z91z96z69v4Do1Gi0Kc0Nc0Sc0Vc0_c0a\
c0dc0ac0_c0<3>PcTNc`PcV<3>VcDXc9Yc4_c0<2>cc0dc0dc0fc\
0<2>gc0gc0ic0ic0ic0kc0lc0tc_zczwcztczrfwogrlknknigpd\
dr`cvXbxSczN<3>gz6hzAizEjzJkzM<4>pz7qz4rz9szDtzHuzKv\
zPwzTwzYwz`wzdzzizznzzpzzlzzgzzdzz`zzYzzTzzQzzMzzJzz\
EzzCzzHzzMzzQzzXzz`zzc<3>zzczz0zz7zzSzzczzczz0<3>zz0\
zz3<2>zz7zz9zz9zzAzzCzzDzzD
}
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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