Fractal visionaries and enthusiasts:

Today's image rates a question mark, which means it's a puzzle.  Is the image a real fractal or an artifact of mathematical imprecision?  The iterated expression that created the image is very simple.  It combines 1/1,000,000 part of Z^(1,000,000) with Z^2, then adds straight C.

I would expect such a combination to produce something like a circle with a Mandelbrot set inside of it, with the circle surrounded by a solid outside.  I would never expect to see things like the two overlapping hairline rings of radius 1, which are centered at the origin and at -1,0, with only a vague outline of a Mandelbrot set inside the ring on the right.  But this is just the kind of trick that would be caused by a breakdown of precision.

It really doesn't matter if the image is a real fractal or an artifact however.  Whatever it is, it was created by numbers, and therefore is at least a pseudo-fractal.

The Mandelbrot shape was given detail by rendering the image with the inside set to FMOD and the proximity set to 0.16.

The name "Real or Unreal" implies the word 'fractal'.  It refers to my uncertainty of the nature of the image.

The calculation time is a nominal 2-1/4 minutes.  Do not be concerned when nothing but dark blue shows up on the screen for a half minute or so.  It takes close to a minute for the detail to appear.

Today here at Fractal Central began with a little sun, but the clouds increased as the day progressed, and by sunset the sky was overcast.  The temperature of 43F +6C was near normal for mid-December.

The fractal cats, always ready to complain, were not happy with the cold draft on their shelf by the window, and spent most of the day watching the humans put up and decorate their seasonal tree.  The humans spent the day doing human things such as working, eating . . . and decorating the tree . . . plus finding fractals and creating word-search puzzles.  One of these days we might strike it rich, but today was not the day.

The next FOTD will be posted in 24 hours.  Until that supreme moment arrives, take care, and if ghosts exist in the mind and the mind exists in the brain and the brain exists in the body and the body exists in the universe, then ghosts must exist in the universe.  But what does the universe exist in, and what exists in the ghosts?

Jim Muth
jamth@mindspring.com


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

Real_or_Unreal     { ; time=0:00:02.15 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=ident passes=t
  center-mag=-0.5/0/0.82 params=0.000001/1000000/1/2\
  /0/0/0/0 maxiter=1000 inside=fmod logmap=yes
  float=y proximity=0.16 symmetry=xaxis periodicity=0
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  5RU5Ug5Xh7Wi8ViAUjBTkCSkERlFRmGQmIPnJOoKNoMMpNMpPL\
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  F0ZF0XG0UG0RG0PG0MG0JG0HG }

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