Fractal visionaries and enthusiasts:

The four-dimensional Julibrot is an abstraction, yet a two-dimensional slice through it becomes as real as today's image.  In effect, we are getting something from nothing -- a big-bang on a microscopic scale.

Today's image is a totally-real oblique slice through the Z^3+C Julibrot.  The corresponding point in the Mandelbrot set lies on the southern shore line of the western branch of the northern seahorse-type valley of the parent Cubic M-set.

I rated the image at a 5-1/2, with 1/2 point of that for the coloring.  The image is mostly of mathematical interest and not all that attractive artistically.  The most interesting feature in my opinion is the way the elements stretch out from the central minibrot in four different directions.  In the quadratic Julibrot they stretch in three directions, so it is not surprising that in the cubic Julibrot they stretch in four directions.

The unlikely values are a sign that the parameters were picked at random by the 'evolver' feature of Fractint.  This feature is of great help in finding the very stretchy orientations in the Julibrot, which tend to be quite critical.

I have calculated a second version of today's image, in which the central minibrot has been un-skewed and un-stretched until it appears almost normal, but in this image the surrounding elements are stretched almost beyond recognition.

The name "Squarely Cubic" refers to the square arrangement of the groups of nine elements surrounding the open area at the center of the image, whatever one might call such an open area.

The calculation time of 3-2/3 minutes is brief enough to avoid excessive impatience yet long enough to allow time for anticipation to build.

The clouds here at Fractal Central on Tuesday were made more enjoyable by the temperature of 75F 24C.  Only a few drops of rain fell, which were not even enough to dampen the sidewalk.  The fractal cats were alert when a stray tomcat wandered into the yard, but after leaving his mark, the intruder moved on without incident.

My day became more interesting when the line leading to the bathroom vanity sprang a leak.  Leaping to the rescue, I repaired the leak before the water rose above the mop-up stage.  All the while FL gave moral support.  The next FOTD will be posted in 24 hours.  Until then, take care, and what's the latest dope on the Theory of (almost) Everything?  Are colliding eleven-
dimensional super-membranes still in fashion?

(The 'almost' refers to the presumably intelligent minds that are searching for the theory.  The last I heard, physicists had neglected to include conscious minds in their 'everything' theory.)

Jim Muth
jamth@mindspring.com
jimmuth@aol.com


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

Squarely_Cubic     { ; time=0:03:42.66-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 center-mag=0/0\
  /2.249922e+009/0.3167/-86.5401900691157948/86.7595\
  921127404353 params=-93.82766624958037/-144.395622\
  7301859/21.19229285561693/-59.73072481460005/-0.06\
  10232505039753/0.7672163526131864/-0.0610232505030\
  753/0.7672163526131864/3/0 float=y maxiter=10000
  inside=0 logmap=505 periodicity=6
  colors=000ULIULIVLFWKAZK6aKFeKOiIXmGeqEnrDwqCooChl\
  D`jDUgEMdEFaF7_F0aG5cHAeFFgDKi8Pk4Um0Zo5cn9plEwiIz\
  gNyeRveQwePucOtdNteMteMraOpZQlWUhTYdQaaMeYJiUGmQDp\
  MArJDqMFpPHoRKmUMjWOhZRf`TccVaeY_i`YkbVndUofSrgQsf\
  SmeUgcVabXW`YP__JY`DXb7Wc1U`1TY1SV1RS1QP1PM1NJ1MG1\
  LD1KA1J71I41H11F32E53C74B949A58C66E65G73I82J86KA9K\
  BDKCGKDKLFNLGRLHULLXMP`MUcMZgMcjOhnRmqWrt`vhfzYlzM\
  lzBkz0ky1jx2iw3hv4gt5es6bm7Zg7Va6T_6Q_6OY6LX6JW5GW\
  5EV5CV5DU5EU4DT4ET4FS4GS4HR4HR7IQAJPDKOFLNIMMLNLOO\
  KePJpQIWRHZSG`TFZUIXULVbzTNzSUUQUXPU_OUXcggKTQJTNH\
  SKGSHESECRADOBERDFREGRGINHJRJKRKLRMNRNORPjURbU7`UC\
  _UIYUNWUTVcYTczSdhQdmOesbazabz`c6cc7cd8ceAceBcfDcg\
  EcgFchzciIciKcjLckMckOclPcmRcmSmnTmoVmoWmpYmqZmq_m\
  ramsbmtdzu3zv4zw5zx6zy8zz9zzAzzBzzDzzEzzFzzGzzIzzJ\
  zzKzzLzzMzzOzzPzzQzzRzzTzzUzzVzzWzzYzz6zzAzzFzzJzz\
  NzzSzzWzz`zzdzzhzzmzzqzzv }

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