Fractal visionaries and enthusiasts:

The formula behind today's image is Z^2+C, the same formula that creates the Mandelbrot set and all its associated Julia sets.  But today's image is obviously not the M-set, nor is it any recognizable Julia set.  It is something I call an Oblate set, a hybrid set half-Mandelbrot and half-Julia.

The X-axis of the image is the real(Z) axis of the Julibrot, while the Y-axis is the imag(C) axis.  The image has a Mandelbrot nature in its vertical direction and a Julia nature in its horizontal direction.  The center of the image is the center of the large period-2 bud of the M-set.  No shape manipulation such as stretching or skewing was done in the creation of the image, though I did add a bit of life by rendering it with the outside set to 'real'.

A most curious relation exists in the location of the elements along the X-axis of the image.  The fractal terminates on the left and right at the points plus and minus 1.61803398875.... which of course is the Golden Ratio, while the two major valleys closest to the center meet at plus and minus 0.61803398875.... which is the reciprocal of the Golden Ratio.  There must be a logical reason why this is so, though I have not been able to find it.

I rated the image at a 7, a good part of which is due to the mathematical interest.  Artistically, the image rates a 5 or 6.  I named the image "A Golden Slice" because of the appearance of the Golden Ratio in it.

Despite all the golden glitter, the image is blazingly fast, finishing on my machine in under 3 seconds, almost as fast as the display can switch to super-VGA mode.

Rain fell most all Monday night here at Fractal Central.  The remaining clouds blocked the sun on Tuesday, but the temperature of 70F 21C was mild enough that the lack of sun was never noticed.  The fractal cats spent an hour chasing a mechanical toy mouse we picked up Monday evening.  Nicholas finally killed it when its battery went flat.  The rest of the day was occupied with routine work.

Remembering yesterday, I dared not ask FL what was happening on the Spanish channel.  The next FOTD will be posted in 24 hours.  It should be no surprise if another odd slice of the Z^2+C Julibrot shows up.  Until then, take care, and let your negative side shine through.

Jim Muth
jamth@mindspring.com


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

A_Golden_Slice     { ; time=0:00:02.85-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0/0.7544715
  params=0/0/90/0/-1/0/0/0/2/0 float=y maxiter=300
  inside=0 outside=real periodicity=6
  colors=000KZzJXwJVsJTpJRmJQjJPgJNeJMbJL`IKYHJVGISF\
  HPEGMDFJCDFBBCA8A958GQKJYKMeKPmKUmKZmKcmKhmKmmIrmF\
  vmCzjHzhNzeSzcXzbTzaPz`Lz_HzZDzZ9zSCzLFzEHz7Kz1Mz6\
  OzAPzFRzJSzNTzSSzXSzaRzfRzhRzjRzlRzmRzoRzqRzrRzzOz\
  zLzzIzzFzzKzzOzzTzzXzzVzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

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