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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image, which is a further development of the theme of yesterday's image, features the MandelbrotVE (variable escape) formula. This formula draws the classic Mandelbrot set, the only added feature being that the escape radius can be set to fractional values. The advantage of setting the escape radius to fractional values is that any midget can be taken and held on the screen while the escape radius is reduced to the point where the midget is swallowed up. Fractals with positive exponents undergo very little change once the escape radius, or bailout, increases beyond the value where all points escape. In the case of the M-set, this radius is 2. But decreasing the bailout below that point progressively cuts off more of the fractal, until finally, nothing but a small featureless circle remains. As the bailout is reduced, a given feature such as a midget remains unchanged at first, but immediately before it is obliterated, the feature undergoes ever more extreme distortion. This distortion, rendered with the <fmod> option, is the basis of today's image. I named the image "Near Escape" because the scene lies very near the reduced escape radius. And I rated it a 6 because in my opinion it is not quite up to the level of yesterday's image. The render time of 9 minutes is acceptable for patient fractalists, but a bit slow for those with other tasks to do. Rendering relief may be found by letting Paul and Scott do the rendering and picking up the finished image from their web sites at: The fractal weather Tuesday was ideal for the middle of winter. Warm sun and a temperature of 52F 11C melted the remaining snow in the yard, and the near calm winds allowed the fractal cats a full afternoon romp. Their only complaint was about the wet ground and the holly trees, which shade the porch end of the yard when the sun is low in the winter sky. This morning it is raining, and the day will be far less pleasant. Without doubt the cats will be far less happy. But that's another story, which I'll tell tomorrow. Until then, take care, and be good but still have fun. Jim Muth jamth@mindspring.com JimMuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Near_Escape { ; time=0:09:46.91--SF5 on a P200
reset=2002 type=formula formulafile=slices.frm
formulaname=MandelbrotVE passes=1 center-mag=-0.74\
585681784166100/+0.11537642028318990/1.955035e+007\
/1/-62.5/2.27705782472609197e-007 params=0/0/0/0/1\
.0777/0 float=y maxiter=5000 bailout=2 inside=0
outside=fmod colors=000NHlPFnRDpSBpTCqTDqTEqTFqTGq\
UGqUHrUIrUJrUKrVLrVLrVMrVNsVOsWPsWQsWQsWRsWSsXTtXU\
tXVtXVtXWtYXtYYtYZuY_uY_uZ`uZauZbuZcuZdv_dv_ev_fv_\
gv_hv_hvZguYfuXeuWduWcuVbtUatT`tS_tSZtRYsQXsPWsOVs\
OVsNUrMTrLSrKRrKQrJPqIOqHNqGMqGLqFKpEJpDIpCHpCHpDK\
oDNoDQnDTnDWmDZmDalDdlDgkDjkCkjCkjCljCljCljCmjBmjB\
mjBnjBnjBnjBojAojAojAoiAoiAoiAoi9oi9oi9oi9oi9oi9oi\
9oi8oi8oi8oi8oi8oh8oh7oh7oh7oh7oh7oh7oh6oh6oh6oh6o\
h6oh6oh6oh7og8og8of9lf9ifAfeBbeB_dCXdCTdDQcENcEJbF\
GbGCaFDbFDbFEcFEcFFdFFdFGeFGeFHfEHfEIgEIgEIgEJhEJh\
EKiEKiELjDLjDMkDMkDNlDNlDNlDOmDOmDPnCPnCQoCQoCRpCR\
pCSqCSqCSqCTrBTrBUsBUsBVtBVtBWuBWuBXvBXvCZwBXvAWuA\
Vt9Us9Tr8Sq8Rq7Pp6Oo6Nn5Mm5Ll4Kk3Il4Jk5Kk6Lk6Mj7Nj\
8Oj9Oj9PiAQiBRiBShCThDThEUhEVgFWgGXgGYfHZfIZfJ_fJ`\
eKaeLbeLcdMcdNddOedOfcPgcQhcQibRibSjbTkbTlaUmaVnaV\
naWn`Xn_YnZciuFTeCTb9T`CRbEPdGNfILhLJj }
frm:MandelbrotVE {; Jim Muth real(c),imag(c)
z=p1, c=pixel+p2,
b=sqr(real(p3)):
z=sqr(z)+c,
|z| <= b
}
END 20.0 PAR-FORMULA FILE==================================
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times.
