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.

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