Fractal visionaries and enthusiasts:  

Today's crazy quilt image is a scene in the East Valley area of the Z^2+C Julibrot.  It is almost a Julia set, since the orientation of the slice is double rotated only 0.01,0.01 degrees from the true Julia direction.

Both Julia and Mandelbrot aspects appear in the image.  The outer shape of the frame shows the Julia aspect of the scene.  The tapering shaft within the Julia frame is a grossly enlarged view of the Mandelbrot valley itself.

In 4-D space an object with two extended dimensions and two tiny dimensions, such as the Mandelbrot elements of the Julibrot, can be enlarged in two dimensions by a properly oriented slice, just as in 3-D space a circular cylinder can be sliced so that the cross section appears as a circle, or stretched in one dimension into an ellipse, or even stretched until it appears as a straight band with parallel sides.

I named the image "Harlequin Hijinks" because of the riotous colors, somewhat resembling a harlequin's costume.

The blocky effect of the image was created by rendering the scene with the outside set to 'summ'.  The calculation time of a mere 40 seconds is a blessed relief from the near-eternity calculation time of yesterday's image.  Little time will be saved by checking the FOTD web sites, but it is still the most convenient way to view the image.

Heavy clouds and a temperature of 41F +5C made things rather unpleasant here at Fractal Central today.  The fractal cats made it through the day uneventfully.  The fractal humans made it through also, but with some left-right disagreement.  The next FOTD will be posted whenever I get a round tuit.  Until then, take care, and watch out for that next door.  It might lead to . . . gulp . . . Room 101.

Jim Muth
jimmuth@earthlink.net


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

Harlequin_Hijinks  { ; time=0:00:40.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/0.891667\
  /1/-90/0 params=90.01/0/89.99/90/0.251/0/0/0/2/0
  float=y maxiter=1800 inside=0 outside=summ
  logmap=1 periodicity=0
  colors=000O0JM0GK0EI0BG09E06C03A018005002000000mz0\
  hz7cz6Zz6Uz5Pz5Kz4Fv4Br38m37h26c25Z14U13P02K01AKdd\
  AKKZCjVAeS9aP8YM7TJ6PF5LC4H93C628314FSbDPZCMVAKS9H\
  O8FL6CH5AE47A257123NXNJSJGNGDID9E9696343bSyZPsWNnT\
  LiQIdMG_JEVGBPD9K97F64A325dN9WI7OD5G938416OF4GA285\
  aIIYBcU9_R8WN7SK6OH5KD4GA3C628314mCxdAmX8cP6UG4K82\
  A3LX1AGBc49Z37U26P24K13F11A0zrmrmcmhUhcJcZHVQEQMCL\
  H9FD7A84542hJRcHO_FMWDJSCHOAEK8CG69C57834412rTanQZ\
  jOWfMTbKRZIOVGLREJNCGJADF8AB68745322XmoO`bGPQ8CDAT\
  G9QE8OD7LC6JA5G95E84C6395274142021khWa_PSRJJIC996I\
  vXGqUFlRDhPCcMB_K9VH8RF6MC5IA4D72951423wM2oJ2hG1`D\
  1UB1M80F50728Er7Cm6Bi6Ae59a48X47T36P35L24G13C12801\
  4bHkZFfVDbSCYOAUL9QH7LE6HA4D738314yIDrGBkEAdC8YA7R\
  85K64D42621zDzuCupBpkAkf9fa8aX7XT6TO5OV_SUbRTeQShP\
  RkOQnOMeKJYHGPEDHBA88705iwibnbWeWQYQJPJDHD686SquER\
  TL6MI5IF4FC3C929616303n0b }

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