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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I named today's image "Pentaheptahexabrot". The outer pentagon surrounding the central minibrot encloses an area with 7-part symmetry, while the minibrot itself has 6-part symmetry. It's an unlikely combination I know, but there it is. Images on the screen do not lie. I could also have included the 2-part symmetry that exists far out beyond the edges of the frame and led me to the scene, but none of this symmetry shows in the image. The scene lies near a larger minibrot near a larger minibrot near a still larger minibrot in the chaos on the bud side of the northern branch of Seahorse Valley of the parent fractal, which on the surface resembles an oversized but otherwise perfect Mandelbrot set. I rated the image at a 7, mostly for mathematical interest. The calculation time of over 12 minutes is admittedly slow, but full relief may be found on the FOTD web site at: Clouds moved in during mid-morning here at Fractal Central on Friday, while the temperature hovered around 54F 12C all day. The fractal cats meowed and resigned themselves early to a sunless afternoon. My day was busy, but not as busy as recent days. The next FOTD will be most likely, but never certainly, be posted in 24 hours. Until then, take care, and if fractals are abstractions, how can it be that we have concrete pictures of them? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Pentaheptahexabrot { ; time=0:12:24.13-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot5 float=y mathtolerance=0.05/1
center-mag=-75.63892599433935/+6.415672693923542/7.\
228203e+010/1/174/0 passes=1 maxiter=6450 inside=255
params=7/100 logmap=1625 periodicity=10
colors=0000_p8ZoBYnEXmHWkKVjOThRSfUQeXPcYKa_ObaRbb\
UcdXce_dgcdifejiellfmofkndjmbim`gl_fkYekWcjVbjTaiR\
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gGbm3gf6f`8eVBdPDcJGU7NKAKADI0FF0ID0KA0N80U20P60LA\
0GE0CI04L06M08M09M0BM0zzz }
frm:DivideBrot5 { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1)+0.00000000000000000001:
z=sqr(z)/(z^(-a)+b)+c
|z| < 1000000 }
END PARAMETER FILE=========================================
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times.
