|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Today's fractal image, which rates a 7, is named "The Richest Fractal". Yes, I realize that the Mandelbrot set is in all likelihood the overall richest fractal, but in the M-set (and the Julia sets) it is not possible to illustrate much of the overall variety in a single image. However, in today's image, which is a scene in a valley of the Z^1.555+C Mandelbrot fractal, much of the variety does appear in a single picture. This is possible because the branch cuts have thoroughly scrambled the original fractal into an omelet of which today's image is a small sample. As is almost always the case in my FOTD fractals, there is a midget at the center. And there are midgets also lurking near the top and bottom of the image. This abundance of midgets is quite unusual in this exponent range, and, combined with the overall variety, makes the image one of the richest of all time. The rating of 7 might be a bit liberal, but a liberal view makes one feel better, so a rating of 7 it is. Enjoy the fractal scene! The render time on my tired old P200 machine is 9 minutes. On a state-of-the-art screamer it will be notably less, but not 1/10th the time. Apparently, the screaming machines with 10 times the cycles per second do less fractal calculation on each cycle. The wait-to-see can be reduced even further by visiting the web site of Paul at: The fractal weather Sunday here at Fractal Central was typical summer fare, with hazy sunshine, a temperature of 93F 34C, and moderately high humidity. The dynamic fractal duo passed the day alternating between the cool indoors and the rather uncomfortable (for humans) outdoors. As for this human, he's about ready to pass the day changing the work to be done into work done. The task will take about 6 hours, so until next time, which will be on the 14th, take care, and keep searching. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
TheRichestFractal { ; time=0:09:15.03--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+0.66148150361188480/+0.368251074896650\
90/798.3305/1/107.5/2.71022093656370089e-012
params=1.555/0/-4.64/0 float=y maxiter=8000
inside=0 logmap=110 periodicity=10
colors=000wMUtLTqKToKSlJSjJRgIRdIQbHQ`DNaHQbLSbPUd\
SXeWZg_`ibckfeljgnmjoqlqunrxpstnsplsljshhsdgs`esXc\
tUatQ_tMZtIXtEVtATt6Ru2Rt3Qs3Pr3Or3Oq3Np3Mo4Lo4Ln4\
Km4JlGIoIDlKIiMMfOQcQVbSZcUadWeeYhf_kganhcqietjgwi\
fugdsfcqdboc`ma_k`Zh_XfYWdXVbVT`USZSRXRPVQOSONQNLO\
LKMKJKIHIHGGGFEKIKOKPRMUVPZZRdaTieWniYshGyl_xtwyps\
wmpujmtgjrdfpacoZ`mWYkTVjQRhNOfKLeHIcCDcEFbGGbHHbJ\
IaLKaMLaOM`QN`RP`TQ`VR_WS_YU__VZ`WZbXZdZYe_Yg`Ymc_\
haYc_WZYVUWTQUSLSQGQPBON7RM9UUAa`8leBhgDehFbiHZjJW\
kLTmNPnPMgRJeUFhTGqSGqRHrRHrQIsPItPJtOJtNKuNKuMLvL\
LvLMwKMwJNxHMzJNxKOwLPvMQuNQtORrPSqQTpRUoSUnTVmUWk\
VXjWXiXYhYZgZ_f_`d``caabbbacc`dc_edZeeZffZggYhgYih\
XjiXkjXlkWmlWnmVonVnoWonVonUonTonSonRpnRpnQpnPpnOp\
nNqnNqnMqnLqnKqnJrmJrmIrmHrmGrmFsmFsmEsmDsmCsmBtmB\
tmAtm9tm8tm7tm7sl9rlBqlDpkFpkHokJnjLmjNljPliRkiTji\
VihXhhZggahh`hi`hj`ik_il_ }
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
|
times.
