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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: After a very pleasant Thanksgiving day, on which I and the fractal lady (who is a great help but wishes to remain anonymous) had the dinner table entirely to ourselves, I ventured into the Mandelbrot set to see what I could find there. My travels took me far out the negative real axis, to a midget around -1.985, where I checked one of the many filaments extending from the little fellow. On the filament, just beyond the point where the broad chaos ends, I found a much smaller midget. The midget reasonably accurately reflects the nature of the broader area in which it lies, but when rendered with the normal equal-iteration-bands method, it lacks a certain something that would give it life. Whatever that missing something is, it was supplied when I tried the 'outside=fmod' option, with the proximity set to a very small 0.00001, and found an image that is different enough to be the FOTD for today. I could rate the resulting image at only a 6 however, because, IMO, the 'fmod' outside option introduces an element of artificiality into the image. Yes, I realize that the equal-iteration-band outside option is also artificial -- all methods of coloring fractals are artificial -- but when I first explored the Mandelbrot set, the flat iteration bands were the only coloring method available, and in my mind, this method represents the 'true' fractal image. The included parameter file renders in 3-1/2 minutes on my machine, and faster on newer units. The wait for the rendering to finish can be replaced by a short pause while the completed image downloads from: The predicted rain failed to arrive here at Fractal Central on Thursday. Instead, the afternoon was partly cloudy with a temperature of 52F 11C, light winds, and scattered happy cats. The cats spent the afternoon in scattered places around the yard, doing nothing in particular other than just being cats. This morning however the rain is most definitely falling. I'll keep the bad news from the dynamic duo as long as possible. I'm not yet sure what kind of day I'll have. It's kind of a holiday made for shopping, but I kind of have some work to do. The only thing (almost) certain is that the next Mandelbrot image will appear in 24 hours. Until then, take care, and who knows what wonders lurk in the land of fractals? (Even the Shadow doesn't!) Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Mandelbrot-16 { ; time=0:03:37.62--SF5 on a P200
reset=2002 type=mandel passes=1
center-mag=-1.98544215780481200/+0.000048925446947\
36/9.506984e+012/1.0005/-167.369632363377747/-0.07\
22266742894553948 params=0/0 float=y maxiter=1800
bailout=9 inside=0 proximity=1e-005 outside=fmod
logmap=yes periodicity=10
colors=020zzXzzXzzXzzYzwbztdzqgzoiznlzknzhpzfszduz\
bxzbzz`zz_zzZzzYzzYzzYzzYzzZzz_zz_zz`zz_zz_zz_zzbz\
zbzxbzwbzudzsdzrdzpdznezlezkezigzghzehzdhzbjz_jzYj\
zXkxVmxTmwRmwMkzPmwTmsXmp_nndnkgngipelpbppYsrXwrTz\
rPzrOzpPzpPznRxnRxnTxmTwmVwmVwkXukXukYuiYuiYsi_sg_\
sgbrgbrfdrfdpfepdepdgndgnainainaip_ep_dr_br_Ys_XsZ\
VuZTuZPuZOwZMwXIxXGxXEzXCzX8zV6zV4zV0zV0zV0zT0zT0z\
T0zT0zR0zT0zT0zV0zV0wV0uX0rX4pZ6lZAkZEg_Ge_Kb_M_aP\
XaTVdVRdYPdbMfdKfgGgiEglAgp8ir4iu0Xu2iwCuxMzzVzzVz\
zVzuVzrVzlVzgVzdVwYVtTVpPXkOXfMX_KXXKXRIYMGYIGYCEY\
6CY2CX6CTCARGAOM8MQ8KT6GZ6Ea4Ai68p6Ak4Cf4C_4EV4GQ4\
GM4IG2KA2K42M22O22K20M20O22O26P28P2AR2ER2GT2KV2MV2\
OX2RX2TY2VY2Y_4_b4db6ed8gd8keAlb2zeAnga_izKgz6kz4l\
z4nz2pz2sz0uz0wz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\
zz0zz0zz0zz0zu0zp0uk0nf0e_0YV2RQ2VO6XO8_MCbMEdKIgK\
KiIOlIPnGTpGVsEYuE_xCdzCe }
END PARAMETER FILE=========================================
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