|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: I saw four green antlers when I studied today's image in search of a name. In a fit of whimsy, I named the image "Antlers in the Treetops". I have no idea how antlers might get in the treetops, since deer do not climb trees, but the name has a nice sound to it, so it will remain. The parent fractal was created by combining decreasing portions of Z^2, Z^3, Z^4 and Z^5, calculating a critical point and entering that critical value as initial Z in the MandelbrotMix3a formula. Actually, there are two critical points visible in today's formula when it is calculated in the parabolic direction. I chose the secondary critical point because lesser critical points often produce the most interesting fractals. Though I have not yet checked the main critical point, I suspect it produces a fairly normal Mandelbrot set. The parent fractal is a vaguely triangular thing with X-axis symmetry. Its eastern part degenerates into non-critical chaos, but an 'East Valley' type feature decorates the west part, while prominent buds with three valleys lie on the north and south edges. Today's scene lies in one of the three valleys of the north bud. The four antlers in the image are spectacular to only an average degree. They therefore rate an average rating of a 5. The render time of 13 minutes is also about average for a F.O.T.D. image. The average download time of the completed GIF file is around one minute. And that download may be accessed at: Wednesday was a hot but dry 90F 32C day here at Fractal Central. The cats were cool as they passed the afternoon resting in the shade of the holly trees. Of course, now that the duo are in their 13th year, resting is just about all they do. Only their location changes. Today is progressing in a similar manner. My tasks for the day begin with the professional work, then shift to fun with fractals. To see the results of that fun, check back in 24 hours. Until then, take care, and be open to new fractal ideas. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
AntlrsInTheTreetps { ; time=0:13:20.15--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix3a function=ident passes=1
center-mag=-1.004490349172/+0.54556575218534/18962\
6.6/1/-15/2.341400962e-010 params=1/2/0.5/3/0.333/\
4/0.25/5/-1.18856877723752/0 float=y maxiter=1200
inside=0 logmap=76 periodicity=10
colors=000msflrelqekqekpdjodjodincinchmchlcglbgkbf\
jbfjaeiaeiadhadg`cg`cf`be_be_ad_ad_ccZdcZecZfcZgcZ\
hbYibYjbYkbYlbYmbYnaXoaXpaXqaXnaXjbXcc2Uh7KmCArH6w\
M7vL7tL7sL8qL8oL8nL8lL9jK9iK9gK9fKAdKAbKAaKB_JBYJB\
XJBVJCTJCSJCQJCPJBOIBNIAMIAMH9LH9KH8KH8JG7IG7IG6HG\
6GF5FF5FF4EF4DEADEFCEKBEPBDUADcRDmZDtfdtdbqcanb`ka\
_h`Ze_XbZW_YVXWUUVTRUROTQLSPIROFQNCPMEQOFRQGRRISTJ\
SVKTWMUYNU_OV`QVbRWcSWeUXgVYhWYjYZlZZm__o`_pa`ma`j\
b`gb`ec`bc`_d`Xd`Ve`SeaPfaMfaKgaHgaEhaBha9ia6ia3ia\
1hbFgcTfdfdadc_bbYaaW_`UY_SXZQVYOUWOTVORTPPSPOQQMP\
QLNQJMRIKRGJSFHSDGSCIUDKWDLXDNZDO_EQaERbETdEUeETdF\
SdFSdGRcGRcHQcHQcIPbIObJObJNaKNaKMaLMaLL`MK`MK`NJ_\
NJ_OI_OI_OJ_NK_ML_MM_LN_KN_KO_JP_IQ_IR_HS_GS_GTbFU\
eEVhEWkDXnCXqCYtBZwA_zA`z9az8az8_zEZzKXzQWzWVz`XzZ\
YzXZzW_zU`zTazRbzQczOdzNezLfzJgzIhzGizFjzDkzClzAdz\
WezYfzZgz_hz`izbjzckzdlze }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <= l }
END 20.0 PAR-FORMULA FILE==================================
|
times.
