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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's image we return to that old warhorse, the overused MandelbrotMix4 formula. But the return is not a noble one, for we have again fallen below fractal average. Try as I might, I could rate today's "Copper Terraces" image, with its muddy terraces, no higher than a 4. The formula that wreaked this minor havoc combines portions of Z^(-1.2) and Z^(2.1) before adding C. I tried to add a little interest by rendering the scene with the inside set to 'bof60' and the outside set to 'fmod', but the improvement was minor. In the end I decided to be stoic and post an image that was not up to FOTD standards. After all, this is hardly the first time a deficient FOTD image has been posted. Thankfully, the image renders in under 6 minutes on my machine, which must be a decade old. In the computer world, this is about as state-of-the-art as a cave-man. On a modern unit, the image will render in a minute or so. And if even one minute is too slow, the completed image can be downloaded from the FOTD web site at: I appreciate the offers of philosophical correction that I sometimes receive from those who wish to convince me that the physical universe really does exist objectively, out there exactly as it appears to our senses. I have been assured that this is true countless times over the past 25 years or so, yet I remain unconvinced. What I need to convince me is some kind of hard proof, which so far no one has offered. Without such proof, the claim that our senses give an accurate image of an objective world remains a postulate, an article of faith with little more validity than my claim that something totally incomprehensible lies beyond the sensual images of a real world. My suspicions that the postulate might in fact be false are only increased by the existence of questions about ultimate meanings that our science is unable to answer. The fact that our senses are subject to illusion is to me another warning that we should not place our total faith in appearances. And the fact that science has already accepted fields, such as the quantum, which cannot be forced into our sensory-produced, intuitive subjective-objective world image, indicates to me that the nature of the world behind the curtain of our senses is not exactly as it appears to us when observed through the senses. How different the world behind the scene might be is open to speculation, but to me, whatever lies there must share at least some of the non-intuitive nature of the quantum things that are assumed to be its building blocks. The sun was bright, but the cold temperature of 23F -5C and the solidly frozen snow pack kept the cats confined to the porch all day Friday here at Fractal Central. When evening came, they demanded extra tuna. Today is starting with hazy sun, cold temperatures, and snow again in the forecast. I suspect the duo will not enjoy the outside conditions. I have a little work to finish and a lot of fractal exploration to do. Until next time, take care, and don't fear the dark. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Copper_Terraces { ; time=0:05:46.15--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+0.84253097446520620/-0.105017701083716\
60/3.373927e+007/1/87.5/6.71509495994704331e-008
params=-0.25/-1.2/0.5/2.1/0/0 float=y maxiter=1200
inside=bof60 proximity=1 outside=fmod periodicity=10
colors=000KyfVDlUGlTJkSMkRQjQTjOWiNZiMbhLehKhgJkgH\
offCvHofGpfFqgErgDsgCthCthBuiAvi9wi8xj7yj6yk7yk9yk\
BxkDwkFvlHvlJulLtlNslPrmUpmZmmcjlhhlmekrbks_jp`gq_\
frZdsXesWbsUYsTWtRTtPRtOPuMMuLKuJHuIFvGDvFAvD8wB5u\
E8tF9sG9rHAqIAoJBnKBmLClMCkNDiODhPEgQEfRFeSFcTGbUG\
aVH`WH_XIYZJXfOWnUrsFrtEquDrqItlOvhUxc_zZeub_q`ZnZ\
YjYXgWWcUV`TUXRTUPTQOSNMRJKQGJPCHO9FN5DM9HN9JN8LN8\
NM8PM7RM7TM7VL6XL6_L5aL5cK5eK4gK4iK4kJ3mJ3oJ2rI2rI\
2qI0qH2pH2pG2oG2nF3nF3mE3mE3lD3kD3kD3jC4jC4iB4hB4h\
A4gA4g94f95e87a89Y7EYDKYJQXQWXWaXagWheXhcYgaZf_`eY\
aeWbdUdcSebQfbOgaMi`Kj_Ik_GmZEnYCoXAqWBoXCmYDj_Eh`\
GebHccI`eJZfKXgMUiNSjOPlPNmRKoRKnRKmRKlRKjRKiRJhRJ\
fRJeRJdRJcRJaSI`SI_SHYSHXSGWSGVSETSESSDRRDPQCOPCNO\
BLNBLMBKLBJKBIKAIKBHLCGMDFNEEOFFPGFQHFRIFSJFTKFULF\
VMFWNFXOFYPGZQI_RK`SMaUObWQcYSd_UeaWfcYge_hgaiicjk\
ekmgloimqjnrjosjptjqujrvj }
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.
