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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is titled "Bad Boy". This name does not allude to a reggae song; it refers to the fact that at one point there are 12 elements surrounding the central midget, which is quadratic in nature and therefore not expected to have rings that consist of a number of elements that is a non-integral power of 2. The image might also be considered bad because it is unstable. The slightest change in the real(p2) parameter causes the entire scene to vanish. Finally, the two satellites in the northeast and southwest corners have six elements surrounding them, which is another wrong number. This image certainly earns its bad reputation. I don't know what it's going to do when they come for it. The generating formula is unusually simple. It takes Z^3 and adds somewhat more than half as much Z^5 before adding C. The resulting parent fractal is rather routine, except when the value of the parameters is near today's, at which point the area of the fractal where today's image lies becomes unstable. Like everything else in the world of fractals, this localized instability happens because of the things numbers do. Given the nature of complex numbers, it could not be otherwise. I rated the image at a 6, a rating that might be considered generous. The coloring is only moderately impressive, and the math interest is worth only slightly more. But then, a 6 is only slightly above average, so the rating will remain. The attached parameter file renders in under 6 minutes on my tired old P200 machine, which might soon be replaced as my fractal-dedicated unit. Those who would rather not wait 6 minutes to see the image may download it, already completed, from Paul's web site at: I continue to find interesting things in variations I am creating of the recently posted Tman formula. Regardless of the number of dimensions, the images are out of this world. In fact, they're in the fractal world. Some unusual images could be coming in the near-future FOTD's. The Fractal Central weather turned milder, but remained too cold on Sunday for the dynamic cats to venture outdoors. There was some sun, but also flurries of snow, and a temperature that never reached freezing. The dynamic ones were surprisingly pleasant in the midst of their confinement. Today is starting milder yet. Could this be the day when the cats' paws reach the turf of the yard? Check in 24 hours to see. Until then, take care, and go where the fractals take you. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Bad-Boy { ; time=0:05:40.20--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+1.09529517003905100/+0.003871516957443\
89/856841.9/1/155/2.75135829397310516e-009
params=1/3/-0.599/5/0/0 float=y maxiter=1200
inside=0 logmap=112 periodicity=10
colors=0004EO4FS3GX3H`2Ie2Ji2Jm6HmAGmEFmHEmLDmPBmT\
AmW9m_8mc7mg5mj4mn3mr2mv1my0mw6cvCUpCPkCLfCHaCCXC8\
SC4NC0ME2MF4MG5MH7MI9LJALKCLLELMFLNHLOIJPKIQLHQNGR\
OFSQESRDTSCUUEXVG_XIbYKeZMhYOk`QldUmhYmkcmnhmpnmrs\
mtrhprclrZhrUdrP`qKXqFTqAPq5Lq0HsAEtKCuU9vc7reDofI\
kgNhhTdjYakbYlhVmmSnrRonRokQohQodPoaPoZXbbcRfjEjq2\
np7npCnoHnoLnoQnnVnn_nncnmhnmmnmqninhfkcbiZ_fUWcPT\
aKPZFMWAJU5PT9UTCZTFdSJiSMnSPsSSi3uj5qj7mk9ikBfkCb\
lEZlGVmISmKOmLKnNGnPDoR9oT5oU2nW6nX9nYCmZFm_Im`Lma\
OibPfbPbbQ_bQWcRTcRPcSMcSIdTFdTBdU8dU7bV7`W7ZW7XX6\
VY6TY6RZ6P_6N_6N_7O_7O_7O`7O`7O`7O`7OaKOaLOaMOaNOa\
OObPObQObRObSOcTOcUOcVOcWOdXPdYQfZPd_Pd`PdaPebPecP\
ecPecPfcPfcPfcPfcPfcPgcPgcPgdPgePhfPhgPhhQhiQhjQik\
QilQimQioRjqSjsTjuUjwVjyWkzXkzYkzZkz_lz`lzalzblzcm\
zcnzcozcpzcqzcrzcszctzcuzcvzcxzcyzczzczzczzczzczzc\
zzczzczzczzczzczzczzczzcz }
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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