Fractal visionaries and enthusiasts:

Today's image takes us on another trip into the abstract fourth dimension.  It is a near-Julia set of the East Valley area of a minibrot located on the main spike of the Mandelbrot set, rather close to the set's main body.

The image is not a Julia set, nor is it a Mandelbrot set.  It is a hybrid, with both Mandelbrot and Julia characteristics.  The outer shape is obviously a Julia set of an East Valley.  The brilliant innermost parts however are a very oblique slice of the Mandelbrot aspect of the area.  The buds in this brilliant area are purely Mandelbrot buds, though at this extreme angle they are partially obscured.

I named the image "Multi-Elephantine" because of an abundance of the beasts hiding throughout the scene, which is chock full of both elephants and bits and pieces of elephants.  In today's image however, the ponderous pachyderms are less apparent than they usually appear.

The rating of a 7 is far enough above average to make the 6-1/3 minute calculation time worth the wait.

Near perfect late summer weather prevailed here at Fractal Central on Monday.  The day began with fog, but by 9am the sun broke through, and for the rest of the day not a single cloud was seen.  The high temperature of 90F 32C was a bit too warm for total comfort in the sun.  The dry air made it quite pleasant in the shade however.

It's too bad we could not spend the day outside in this perfection.  The fractal cats enjoyed their perfection however.  They found perfection on the kitchen floor and on their shelf in the sunny window -- while the sun was not there, of course.

The next FOTD will be posted in 24 hours.  Until then, take care, and why philosophize about the meaning of existence, when we don't even know the meaning of fractals.

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


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

Multi-Elephantine  { ; time=0:06:22.13-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1 maxiter=32767
  center-mag=0/0/38/1/90/0 params=89.96/0/89.96/0/\
  -1.416653/3.1e-005/0/0/2/0 float=y
  inside=0 logmap=28 periodicity=7
  colors=000AFUAGWAHYAI_AJaAKcALeBMgCNiDOkEPmGQoIRqK\
  SsMTsOUpQVkSWfUXaYYX_ZRa_Mc`HeaCgb7ic2kd7meBofFmgK\
  lhOkiSijXhk`gkdddYbZR_TLYMEVG7TA1WB7ZCDaCIdDOgDTjE\
  ZmFdpFisGouGtqFpmEmjDjfCfcBc_A`X9XT9UP8RM7NI6KF5HB\
  4D83A427124HVPXwhYteYqcYnaZk_ZhYZeW_bU_`U_YU_VU_SU\
  _TUZUUZVUZWUZXUZYUZZUZZUZZVZZWZZXZZYZZZZZ_ZX`ZZ_ZZ\
  ZZZYZZXZZWZZWZZXZZYZZZZZ_ZZ`YZaXZbWZcVZcU_cQ_cN`cQ\
  acSacU`cWZcYXc_VbaT`dQYfOVgMShKQiINjGKkEIlGIlIIlKI\
  nLIoNIpPIrRIsSIsUItWItYItZIu`IubIucIqaJn`KkZLgYMdX\
  NaVOZUPVTQSRRPQSLPTINUFMVCLVNTOX_HffBgdGgcLgaPg`Uh\
  _ZhYbhXghWkfZieagdcecfdchbck`cm_clackbcjcciechfcgg\
  cficejcdkcdlcckcbkcakc`jc_jcZjcYicXicWjcVkcVlcWmcX\
  ncYocZpc_qc`rcascbtccuccvccwccxccycczcczcczcczcczc\
  czcczcczcdzcezcfzcgzchzcizcjzckzclzcmzcnzcozcpzcqz\
  crzbszatz`uzZvzXwzVxzTyzRzzQzzOzzMzzKzzIzzGzzFzzDz\
  zBzz9zz7zz5zz0zz1zz1zz1zz }

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