Fractal visionaries and enthusiasts:

Today's image is a slight reworking of an image I posted a couple years ago.  It lies in the parent fractal that comes about when straight Z is subtracted from Z^(2.5) and straight C is added on each iteration.

This parent resembles a Mandelbrot set caught in the process of morphing into a hammerhead shark.  It has three large connected bays where its main bud would be expected.  Today's image lies in the valley separating the north bay from the middle bay.

The name "Butterfly Cookies" refers to the four brilliant electric blue elements surrounding the central minibrot.  Only a little imagination is needed to turn them into butterflies.

The rating of 8-1/2 is not exaggerated.  I really do think the image is worth it.

The calculation time of just under 1-1/2 minutes will pass rapidly once the first rough rendering appears on the screen.  And as always, the FOTD web sites will eliminate all need of rendering.

The day began with fog and low clouds here at Fractal Central.  By 10am the clouds broke to let through enough sun to make the afternoon reasonably pleasant, with a temperature of 79F 26C.  Showers occasionally threatened, but as of post time, nothing had fallen at FC.

The fractal cats were peaceful enough.  We humans have vague plans of screening in the FC back porch and turning it into an outdoor cat sanctuary, but so far the plans remain quite vague.  The next FOTD will appear soon.  Until then, take care, and be alert for hit-and-run Julia sets.

Jim Muth
jimmuth@earthlink.net


START PARAMETER FILE=======================================

Butterfly_Cookies  { ; time=0:01:25.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=ident
  center-mag=-0.1607468368364147/+0.1293682935344705\
  /4654329/1/145/0 params=1/2.5/-1/1/0/0/0/0 float=y
  maxiter=1200 inside=0 logmap=154 periodicity=6
  colors=00000500720740852874A87AA8CCACDDDFFDHHFIKFK\
  LFLMFMOFOPFPRDRSCSUAUV8VW8WZ7Ya5Zd4`g2ai2cl0do0eoU\
  goUhlSeiScgRZdRVaPRZPLWOHUOCRM7OM2LMHIWSHecDomCxkA\
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  4RK5VL7ZL8aMAeMCiODmPFqPHtRIxSKzSLzU9pWFzUMzRSzOYz\
  LdzIizFozItzLzzZzzlzzlzzZzzLyzIqzOizUazZUzdLzLCyLF\
  yLIZLLZLOZURsPUoMWiKZeFa`CdW0dU8gSHhROiPVlOamMhoLo\
  pKusIztHzuFzwzpzzzzzzhzzizzkzulqomlhoggm`coa`oaYoc\
  VocSodPodModKoeHoeDogAog7oh4oh0mk0oh5pe8pzAmzAkzAh\
  zAezCczzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzFC8OIIVMRaSZh\
  Wgo`ouewzizzmzxFlsImmKmiLodMo`OoVPpRSpLUqHVqAWq5Ys\
  0Zs0`s2ctAduHgwOhxUky`lzgozlpzsszxtzqpwlmpgki`hcVd\
  WPaPLZILZAZZ0ZZ2ZZ2lZ2lZ2lZ2lZ2lZ2lZ2lZ2lZ2yZ2yZ2y\
  Z2yZ2zZ2zZ5zZ7zZAzZCzZAzZ8zZ7ye5yl4yl2yl0ys0yy0yz0\
  yz0zz0zz0zz0zz0zz0zz4zz7zzCzzHzzKzz0zzDzzZzzszzpzz\
  mzzkzzhzzezzczzazz`zzZzzY }

frm:MandAutoCritInZ {; 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)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

END PARAMETER FILE=========================================