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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In today's FOTD image I have tried to recreate the essence of the image that was originally intended for yesterday's FOTD honors. As the rating of 7 shows, today's substitution does a fair job of recreating what is irretrievably lost, but the original effort was quite a bit superior, rating at least an 8. I had three clues in my effort to recreate yesterday's lost image -- I remembered that the formula was number 5 in my series of 12 MandNewt formulae, the function was 'atanh', and the inside fill was bof60. Having no idea of the numerical parameters, I drew a blank image with all parameters set to zero and let the Fractint evolver enter numbers at random. After several hundred rejected thumbnails passed by, one appeared that bore at least a modicum of resemblance to the lost fractal. When I further explored the likely candidate, I found scenes similar to but not exactly like the one that was lost. I have named today's picture "An Ikenaga Quantum". 'Ikenaga' is the name of the inventor of the Ikenaga function, a function which is still somewhat of a mystery, and variations of which appear in all 12 of my MandNewt formulae. A quantum of course is a specified amount of something, often assumed to be the minimum possible amount. One molecule of water, or one photon of light, are examples of quanta. No such things exist as 1/2 molecule of water or 1/2 a photon of light. I gave today's image the 'quantum' name because it has a kind of sub-atomic aura about it. It's an image that would look far better in true-color, but since true-color is not yet a working feature of Fractint, we'll have to satisfy ourselves with the un-true 256-color GIF version. The 2-minute render time of the parameter file is reasonable, and running the file is the best way of viewing the image. One alternate method of viewing the image is to wait 16 hours until the GIF file is posted to the Usenet binary group: The fractal weather today was very unpleasant, with a cold rain most all day, which became mixed with sleet late in the afternoon, and changed to snow at nightfall. The temperature of 34F (1C), combined with the wet conditions, kept the fractal cats sleeping by their radiators most of the day. It's now time for me to settle into my favorite chair to watch the junkiest old sci-fi movie I can find. If I can't stay awake through the whole thing, so much the better. The next FOTD is only 24 hours from now. Until then, take care, and if fractals were alive, would they be animal, vegetable, or mineral? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
An_Ikenaga_Quantum { ; time=0:02:08.86 -- SF5 on a P200
reset=2001 type=formula formulafile=mandnewt.frm
formulaname=mandnewt05 function=atanh passes=1
center-mag=+0.59043327144988720/-0.56548623104432090\
/72.76091/1/44.998
params=3.59/0.73/0.88/1.64/2.11/0.26 float=y
maxiter=125 inside=bof60 logmap=yes periodicity=10
colors=000_azaazdazi_zk_zpYzsYzxUzzUzzSzzSzzPzzPzzRz\
z_zzczzhzzozztzzxzzzzzzzzzzzzzzzxxzuszunzsiypfvparnY\
okSkkNgiLciG_fBVd6Rd1Oa0K_0G_0BZ06X03U00S00S<3>00I33\
88G6GS1LY0Sa0Yf0dk0ip0pu0uz0zz0zz0zz0sz0kz0dx8YuIPsP\
Ip_Bni3kp0iz<2>0az0az0Yz3SzLNiaISuDBz80z30z10z30z30z\
60z60z80z80z80uB3nB8iDDaDIUDPPGUIG_DId6Ii0In0Ls0Lx0N\
z0Nz0Nz0Nz0Pz0Pz0Pz0Sz0Sx0Uu0Us0Up0Yn0Yk0Yi0_i<3>0_i\
0_i0_i0_iLLUd6Gx03u01<8>u00u00u00<2>u10u10u30<3>u30z\
10<2>z01z08z0Dz0Iz0Pz0Uz0az0fz0k<2>z0su1sk6u_BxPDxDI\
z3Nz0Sz0Yz0az0dz<3>0xz1zzBzzIzzSzz_zzfzzdzz_zzYzzSzz\
PzzSzzUzzUzzYzzYzz_zzazzazzdzzdzzfzzizzizzkzzkzznzzn\
zz<3>dzzazz_zzYxzUuzSszPnz<3>GdzDazB_z8Yz6UzBazGizIp\
zNxzPzzUzzYzzSzzNzzLzzGxzDsz8nz3iz1dz0_z0Uu0Pp0Ln0Gi\
0Bd06a01Y00U00S01P<3>0BG
}
frm:mandnewt05 {; Jim Muth
z=c=fn1(pixel):
a=z^2+(c-p1)*z-c
b=p2*z^2+c-1
z=z-1*a/b
p3 <= |a|
}
END 20.0 PAR-FORMULA FILE==================================
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times.
