Fractal visionaries and enthusiasts:

The minibrot in today's image does not really exist.  Yes, I know it can be seen in the image, hovering mystically above an alien horizon, but is it really there?  I think not.  Since the minibrot consists totally of 'inside' stuff, it is a virtual-virtual thing in the virtual world of fractals.  Anyone who doubts this can change the 'inside' setting from the 'bof61' of the image to 'numb' and observe the incredible vanishing minibrot.

The parent fractal came about when I subtracted a very unlikely portion of Z^(0.45) from an equally unlikely portion of Z^(0.76), then added C on each iteration.  When rendered in the usual manner, this parent fractal is certainly the least promising fractal in FOTD history -- an egg-shaped oval with a pinched-off west edge, straight edges devoid of any detail, and a blank inside.  But in fractal land things are not always as they seem, and the apparently blank inside of this parent holds a surprise.

The surprise lies at the point where the X-axis crosses the eastern edge of the parent fractal, where a tiny minibrot lies hidden, an etheric thing that barely exists in the empty inside of the parent.  This minibrot is revealed by the active inside fills, especially the 'bof61' of today's image.  The 'fmod' inside option also creates an interesting image, and this image may be adjusted by changing the proximity factor.

The rating of a whopping 9.5 reflects the surprise I felt when I found the hidden minibrot.  It also includes the standard half-point for the coloring.  It might have rated a perfect 10 if I had not posted a different version many years ago.  The name "The Mystic Minibrot" was inspired by the overall feeling of the image -- that of a strange alien landscape with mystic forces invisibly at work in the infinite blue depths of the sky.

The image is a very fast one, finishing in 42 seconds on the 200mhz machine and an estimated 12 seconds on the 2000mhz unit, which is currently out of action, and will remain out of action until I get a chance to try some of the suggestions I recently received from the list.

Heavy clouds darkened the sky here at Fractal Central all day today.  And to make things worse, light but steady rain fell most of the time, keeping things unpleasantly wet.  The temperature started at 52F 11C at daybreak, but fell through the day to 43F +6C at post time.  The fractal cats were totally disgusted with these conditions, and spent the time pondering what kind of distracting trouble they might get into.

The humans had a rather busy day, which is good for the pocketbook if not the soul.  The next FOTD will be posted in 24 hours.  Until then, take care, and would the Mandelbrot set exist if we had never invented complex numbers?  Did the world vanish when men showed that our concepts of atoms are mental models based on the quantum math, and that there are no actual tiny solar systems down there, with real balls circling a real bubbling raspberry like planets circling a sun?

Of course it did not!

Jim Muth
jamth@mindspring.com


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

The_MysticMinibrot { ; time=0:00:12.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=ident
  center-mag=+0.01221343/0/557/1/-90/0 float=y
  params=1.9608526/0.76/-0.4602001/0.45/0/0/0/0
  maxiter=95 inside=bof61 logmap=yes periodicity=6
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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=========================================