Fractal visionaries and enthusiasts:

Yesterday's image showed one of the frequently mentioned but rarely seen fractal 'fans' that exist in fractals of the type (-n*(Z^-n))+(-n*(Z^-n))+(1/C).  Today we check one of the minibrots that exist around the edges of such fans.

In today's image we doubled the (Z) portions of the FOTD of November 23.  The resulting parent fractal closely resembles the earlier image, though its size is slightly smaller.

Today's image is located on the right edge of the 'fan' that was featured in yesterday's image.  The overall effect is of a minibrot in one of the higher-order 'stars' of the Mandelbrot set.  There are also minibrots all over the flat 'blade' of the parent fan, though it takes a bit of searching to find them.

The name "Near the Optimum" is misleading.  I see nothing in the image to imply that something in it is near optimum.  In fact, I doubt that anything in fractals can be considered at optimum, except perhaps for a critical value for initial Z in certain fractals.

The rating of only a 7 means that calculation time of 16-1/2 minutes will be more effort than the result will be worth.

The finished image is or soon will be posted on the FOTD web site at:

       http://www.Nahee.com/FOTD/

If the image is not yet posted, be patient.  Paul is doing his best to get the FOTD site caught up, but he is still recovering, and it might be a while before things are completely back to normal.

Saturday brought snow flurries, but with some afternoon sun, and a temperature of 39F +4C to Fractal Central.  The snow flakes brought the fractal cats to the window, but they soon grew bored and returned to warmer spots.

My day was average.  The next FOTD will be posted in 24 hours.  Until then, take care, and if we could change the past, would we know the future?

Jim Muth
jamth@mindspring.com


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

Near_the_Optimum   { ; time=0:16:32.05-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandAutoCritInZ function=recip float=y
  center-mag=+1.934869010826633/-1.863451620247872/\
  1.059113e+010/1/-167.5/0 params=-22/-1.1/-5.5/-11\
  /0/525/0/0 maxiter=12000 inside=255
  logmap=2000 periodicity=6
  colors=000UGVXKSZOP`RMcVJeTGgXDiVBa_PUWbMSoPUmRVlU\
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  PmzUmzZmzcmzhmzmmzmmzmmzmmzmmzmrzmrzmrzmrzmrzmrzmr\
  zmrzmrzmrzmrzmrzmrzmrzzzz }

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