FOTD 18-12-14 (Point of Attraction [A-6,M-4])

19 Dec 2014

      FOTD -- December 18, 2014 (Rating A-6,M-4)

Fractal visionaries and enthusiasts:

The Mandelbrot set is a single two-dimensional slice through a 
four-dimensional figure known as the Julibrot.  Being 
four-dimensional, this figure can be sliced in an unimaginable 
number of ways, many of which, like today's strange image, bear 
no resemblance to the Mandelbrot set.  I named this strange 
slice "Point of Attraction" because it lies so close to the 
Julibrot convergence point at -0.75 real(C), 0.5 real(Z).

The art rates a fair 6, mostly because of my extra effort at the 
coloring.  The math rates a humble 4, since there are no new 
ideas in the math.

The calculation time of 5-3/4 minutes borders on slowness, but 
the web sites can solve this problem.

The finished image is posted at:

      <http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

       <http://www.Nahee.com/FOTD/>

  <http://user.xmission.com/~legalize/fractals/fotd/about.html>

Heavy clouds and a temperature of 36F +2C kept things suppressed 
here at Fractal central today.  The suppression included both 
the fractal cats and humans.  The next FOTD will be posted 
somewhere between one and four days from now.  Until whenever, 
take care, and ignore that world out there behind the curtain.

Jim Muth
jimmuth@earthlink.net

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

Point_Of_Atraction { ; time=0:05:45.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1 center-mag=0/\
  -0.03954/24.15395/0.2773 params=0/0/90/0/-0.752/0/\
  0.5/0/2/0 float=y maxiter=3200 inside=255
  logmap=-88 periodicity=6
  colors=0000000000000000000000000000000000000000000\
  0000000000100200300400500600700800900A00A00A00A00A\
  00A01B02B03B04B05B06B07B08B09B0AB0BB0CB0DB0EB0FB0G\
  C0HC0IC0JC0KC0LC0MC0NC0OC0PC1QC2RC3SC4TC5TC6UF7UH8\
  UJ9VLAVNBVPCWRDWUEWWFXYGX_HXaIYcJYeKYhLZjMZlNZnO_p\
  P`rQatPbuPcuPdmPemPfnPgoPhpPiqPjsPkuPlwPmxPnyPozPp\
  zPqzPrzPszPtzPuzPvzPwzPxzPyzPzzPzzPzzPzzPzzPzzPzzP\
  zzPzzPzzOzzPzzPzzQzzQzzQzzRzzRzyRzxSzwSzuSzsUzqWzo\
  Yzm_zkaziczgeqegqciqakq_mqYoqWqqUtqTwqSzrQzrPzrOzr\
  MzrLzrKzrIzrHzrGzrEzrDzrCzq6zrBzsGzsLztPztUzuZzvbz\
  vgzwlzwpzvnzumztlzskzsjzrizqhzpgzpfzodznczmbzmazl`\
  zk_zjZzjYziXzhWzgUzgTzfSzeRzdQzdPzcOzbNzaMzdKzaLzZ\
  LzWLzTLzQMzNMzKMzEDzGIzIMzKQzMUzOYzQazSezUizVhzVgz\
  VgzVfzVezVezVdzVczWczWbzWazWazW`zW_zW_zWZzXYzXYzXX\
  zXWzXWzXVzXUzXUzYTzYSzYSzYRzYQzYQzYPzYOzZOzZNzZMzZ\
  MzZLzZKzZKzZJz_Iz_Iz_H90K }

frm:SliceJulibrot4   {; draws all slices of Julibrot
  pix=pixel, u=real(pix), v=imag(pix),
  a=pi*real(p1*0.0055555555555556),
  b=pi*imag(p1*0.0055555555555556),
  g=pi*real(p2*0.0055555555555556),
  d=pi*imag(p2*0.0055555555555556),
  ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
  sg=sin(g), cd=cos(d), sd=sin(d),
  p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
  r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=z^(real(p5))+c
  |z|< esc }

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

Jim Muth

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