Fractal visionaries and enthusiasts:  

Today's image is named "Broken Perfection".  The reason for the name is readily apparent in the image, which shows an almost perfect ring around a minibrot.  The ring resembles a donut-shaped planetary nebula puffed off from a dying star, but look closer.  The ring is broken on its east side by a discontinuity that is caused by the fractional nature of the Z^(10.5) exponent and extends all the way to the central minibrot.

The 9-1/2 bays of the minibrot point to an exponent of 10.5, while the 10-1/2 elements in the ring confirm the deduction.

The location of the scene is at the edge of a larger but still order-10.5 minibrot on the main spike of the parent Mandelbrot set, just east of the prominent large quadratic minibrot.

The art rates a 7, mostly due to the modicum of extra effort I put into the coloring.  I could rate the math aspect no higher than a 6, especially after noting that we have been exploring this math trick for over a week.

The calculation time of merely forty seconds makes up for any deficiencies however.  This time will pass faster than Ali Baba's forty thieves.  But there is no danger, since the web sites will keep the thieves at bay, at least for those who choose to take shelter there.

Heavy clouds and light rain spoiled things here at Fractal Central today until the sun broke through in mid-afternoon.  The temperature of 68F 20C was mild enough, but with the house heat turned down, the fractal cats would have preferred more sun.  The humans had a thoughtful day.  While I was out walking, I noticed that the trees in the town square are still as bare and bleak as in midwinter, and it's only one week until the month of May, when trees are usually in full leaf.

The next FOTD will be posted in 24 hours or whenever.  Until then, take care, and at this Easter time I hear of a decline in religious faith.  The decline is nothing new, but could it be driven by the fact that among the over-educated, religious faith is widely seen as a vestige, which is now little more than a comforting diversion from reality clung to by the under-educated and easily disproved by scientific study and rational thought?

Jim (both Theist and Atheist) Muth
jimmuth@earthlink.net


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

Broken_Perfection  { ; time=0:00:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=findivbrot-2 function=recip inside=0
  center-mag=-1.741394475156175/+0.00000405269130397\
  /2.773655e+012 params=10.5/1e+020/0/0 float=y
  maxiter=400 periodicity=6 mathtolerance=0.05/1
  colors=000zdkzmsznlznezo_zoTzoNzoKzoHzfFzZDzRBzJ9z\
  B7z35z4Ez5Mz6Uz7az8izA4z9Ez8Oz7Yz7fzEczKazRZzXXzcV\
  ziSzpQzvOzqQzmRzhTzdUz`WzWXzSZzPYzO_zN`zMazLbz5xzD\
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  ouulsthqsbprZoqWlpTkoQjnNimKhlHgkIfjJeiKdhLcgMbeNa\
  bO`_PZYQXVRUTSPQQLOLJLJGJGEGDAEB9CA79757725404NA4T\
  F4YK4bP4gU4kb4ph4vo4zv4zzcztevtxjowZjwOfwVMbW1IU3K\
  S5LQ7NP9ONBQLDRKFTIGUGIVFKXDMYBO_AQ`8Sb6Uc5Vd6Ue6T\
  ezSezRezQezPezOezPdzQdzQdzRdzSdzUdzVdzObzSczWdz_ez\
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  zouznszmqzlpzknzjlztnzolzjkzfizahzXfzTezOczKbzO_zR\
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  IazISzIIzFGzDEzBCzKKzTSzzzzX`zS`zN`zI`zD`z8`z4`z5U\
  z6Oz7Hz8Bz85zCBzFGzIMzLRzOXzRazUgzXlz0mz7kzEizLhzS\
  fzZdzdczSUzGLz4CzELzNUzWb }

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