Fractal visionaries and enthusiasts:

Today's image is named "The Inner Circle".  The name has nothing to do with a secret society; it refers to the unusually well defined order-23 minibrot that nearly fills the frame.

Actually, the minibrot has some mathematical difficulties.  The minibrot itself has 22 lobes, which is just what would be expected; and there are 23 peach-colored elements immediately surrounding the minibrot, which is just as it should be.  But beyond here things go drastically wrong, for there are only 20 fractal arms radiating from the minibrot, and this is certainly not the number of arms that should be there.

The scene is located in the period-10 radical on the southeast shore line of the parent fractal, which on the surface is a perfect Mandelbrot set.  I assume that the period-10-ness is somehow mixed up with the order-23-ness to create exactly 20 arms, though regardless of how I combine the numbers, I can't make it come out right.

It really doesn't matter however.  The minibrot by itself is impressive enough to rate a 7, which is no small feat for a fractal that is basically a glorified circle.

The image is also filled with numerous anti-minibrots.  I might dredge up one and present it as tomorrow's FOTD.

A morning shower was followed by partly cloudy skies, lower humidity and a temperature of 86F 30C here at Fractal Central on Thursday afternoon.  The fractal cats agreed -- they stretched on the tile floor and slept until the sun went down.

My day was busy; FL's was the same.  The next FOTD will be posted in 24 hours.  Until then, take care, and they say that nothing can escape a black hole.  If this is so, how does the gravity escape?  (It's an obvious question that I have never seen satisfactorily answered.)

Jim Muth
jamth@mindspring.com
jimmuth@aol.com


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

The_Inner_Circle   { ; time=0:02:58.07-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=FinDivBrot-2 function=recip
  center-mag=+0.334957790435/-0.046732876989/3.1e+008
  params=23/1e+050/0/0 float=y maxiter=3200 inside=0
  logmap=400 periodicity=6
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  zzHzzHzzGzzFzzFzzEzzDzzCzzCzzBzzAzzAzz9zz8zz7zz7zz\
  6zz5zz5zz4zz3zz2zz2zz1zz0 }

frm:FinDivBrot-2   { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }

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