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November 10, 2010: The Mystical Donut Nov. 9 Nov. 11 2010 FOTD Home
 Rating 7

donut

Fractal visionaries and enthusiasts:

Like all images in the month of November, today's image lies in an unfamiliar slice of the Z^2+C Julibrot.  I'll not try to describe the location or orientation of the parent-fractal slice, other than reporting that it is centered on Seahorse Valley and is double-rotated halfway between the Mandelbrot and Julia orientations.  This is little help, since in the 4-D Julibrot there are countless orientations halfway between the M and J directions.  Today's scene is located on the rudimentary main stem of the parent slice.

I named the image "The Mystical Donut".  I know it's a rather silly name.  There is little of a mystical nature in a donut.  But I can't help it if I saw a donut in the image.

Most of the image's detail was created by rendering it with the outside set to 'real'.  The 'imag' and 'summ' options work almost as well.

The rating of a 7 makes the image worth the minute required to run the parameter file.

Those with over-qualified machines can hopefully find the eye-ball-ready image posted to the FOTD web site at:

      
http://www.Nahee.com/FOTD/

A mixture of sun and clouds prevailed here at Fractal Central on Tuesday, with the clouds predominating.  The temperature of 55F 13C was just a bit too chilly for maximum comfort, though it was about normal for early November.  The fractal cats enjoyed the sun when it appeared and sought comfort by the heat when it went behind the clouds.

My day was average.  Isn't that boring?  The next FOTD will be posted in 24 hours.  Until then, take care, and do our egos exist when we are unconscious?

Jim Muth
jamth@mindspring.com


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

The_Mystical_Donut { ; time=0:01:03.50-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot2 center-mag=-1.41420407/\
  0/724383.1/1.5564/-90/0 params=45/0/-45/0/-0.75/0\
  /0/0 float=y maxiter=1400 inside=0 outside=real
  colors=000JffIeeIddIccIbbIbaIb`Ib_IbZIbYIbXIbWIbVI\
  bUKaTLaSNaROaQQaPSaOTaNVcMXeLYgK_iK`kKdmKhoKmqKrsK\
  vs2zz2zzzzzzzzzzzzvuzrw2my2hz2ZoCUeMPVWKLfGApCAzB8\
  vB6tB4rB3oB3mA4kA4iA5gA6eA6dA7c97b98a98`99_9AZ9AY8\
  BX8BW8CV8CU8DT8DS7ER7EQ7FP7FO7FN7GM7GL7GN7HP7HS7IU\
  7IW6IZ6J`6Jb6Je6Kg6Ki6Ll6Ln6Lp6Ms6Mu6Mw8Nv9OuAPtBP\
  sCQrDRqERpGSoHTnITmJUmKVlLVkMWjOXiPXhQYgRZfSZeT_dU\
  `cV`cSZdQYeOXeMWfJVgHUgFThDRiBQi8Pj6Ok4Nk2Ml0Ll2Nh\
  3Od4Pa5QY6RU7SR8TN9UJAVGBWCCX8DY5BaDAeL9iT8l`AmaBm\
  bDmcEmdGmeHnfJngKnhMniNnjOnkQolRomTonUooWopXpqZpr_\
  psaptbpucpuensflrgkqhipigojfnldlmcknajo_ipZhqXgrWf\
  n_djbcffabi`Zm_VpYRtXOwWNtVMqVLoVKlVJjUIgUHeUGbUF_\
  UEYTDVTCTTBQTAOTCPUDQUERUFSUGTUHUVIVVJWVKXVLYVNZWO\
  _WP`WQaWRbWScXTdXUeXVfXWgXVeUVcSVbQV`OV_MVYKUXIUVG\
  UUEUSCURAUP8UO6SSDQWKP_QNcXMgbKkiJnoKnpKnpKnpKnpKn\
  oKnnKmmKllKkkKjjKiiJhhJgg }

frm:SliceJulibrot2   {; 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),
  c=p+flip(q)+p3, z=r+flip(s)+p4:
  z=sqr(z)+c
  |z|<=9 }

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