Fractal visionaries and enthusiasts:

Today's image shows two overlapping minibrots.  Actually, they can not properly be called minibrots, since they are larger than the Mandelbrot set itself.  But whatever one might call them, (Mandeloids would be more correct.), they are two of the most unusual fractal 'objects' I have yet stumbled upon.

The generating expression is quite simple.  It combines 0.4 negative parts of (1/Z) with 0.4 positive parts of Z^(2) before adding (1/C).  The resulting fractal is little more than an oversized field of chaos, with today's curious scene lurking in the center, needing special coloring to make it fully visible.

In some fractals, minibrots appear to be merging.  When they do, it is always the same parts of the minibrots that join.  Today's image however makes no sense at all.  The mandeloids are not merging; they overlap in quite a curious way.  In the areas where the top Mandeloid lies over the underlying one, it is skeletal, a ghost that lets the one under it show through.  In other areas it is solid.

The brownish bits and pieces in the foreground are arranged with no symmetry at all.  The brilliant blue Mandeloids in the background are almost but not quite symmetrical with respect to the X-axis, which with the image rotated 90 degrees, runs vertically through the center of the frame.  I would not speculate which if any parts of the scene are actually critical.

I declined to give the image a rating, since I have nothing previous to compare it to.  The name "Overlapping Minibrots" explains itself once the image is seen.  The calculation time of 1-1/2 minutes assures that no hurried fractalist will feel the pangs of impatience.

Yesterday's foul weather continued into the morning here at Fractal Central.  The fractal cats were too interested in laying claims to the new chair to be concerned with the occasional rain and relatively mild temperature of 50F 10C.  FL and I had a day of preparing for the traditional Thanksgiving feast tomorrow.  I would just as well do away with feasts, but what the heck.  We have to do something to occasionally break the everyday routine.

Unless the Thanksgiving feast gets totally out of control, the next FOTD will be posted in 24 hours.  If control is lost, the next fractal could be delayed a short time.  Until whenever, take care, and I wonder who is paying for those supposedly historical but actually Christian doctrine shows that appear so frequently on the so-called 'science' and 'history' channels.

Jim Muth
jamth@mindspring.com


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

OverlapingMinbrots { ; time=0:01:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=recip passes=1
  center-mag=2.13391/0/0.2282051/1/90/0
  params=-0.4/-1/0.4/2/0/0/0/0 float=y maxiter=4200
  inside=0 logmap=9 symmetry=none periodicity=6
  colors=000HBAHBAHAAHAAHAAHAAH9AH9AM9AM9AM8AM8AL8AL\
  8AL7AL7aL7aL7aL6bL6bL6bL6cL5cL5cL5dL5dL4dL4eL4eL4e\
  L3fL3fL3fL3gL2gL2gL2hL2hK1iL2hL2hL3gM3gM3fM4fM4fN4\
  eN5eN5dN5dO6dO6cO7cP7bP7bP8bP8aQ8aQ9`Q9`Q9`RA_RA_R\
  AZRLIRLIRLIQLIQLIQLIQLIQLIQLIQLIQLIPKJQLIQLIQLIQLU\
  QMURMURMURMURMURNUSNUSNUSNUSOUSOUSOUTOUTOUTPUTPcTP\
  cUPcUQcUQcUQcUQcVQcVRmVRmVRmVRmVSmWSmWSmWSmWSzWTzX\
  TzXTzXTzXUzXUzYUzYUzYUzYVzYVzYVzZVzZWzZWzYBzXBzXBz\
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  UrJUrJUrIUrIUrHUrHUrHUrGUrGUrFUsGUrGmrGmqGmqGmqGmp\
  GmzGmzHmzHmzHmzHmzHmzHmzHmzXmzXmzWmzWmzVmzVmzVmzUm\
  zUmzTmzTzzSzzSzzSzzRzzRzzQzzQzzUzzUzzUzzUzzUzzUzzU\
  zzUzzczzczzczzczzczzczzczzczzmzzmzzmzzmzzmzzmzzmzz\
  mzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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=========================================