Fractal visionaries and enthusiasts:

Very slow image alert!!   Run parameter file at your own risk!

We have not had a FOTD theme month for quite a while, so I have decided to make Seahorse Valley the FOTD theme for the month of June.   Not only will we explore the well-known Mandelbrot and Julia aspects of the valley, we will check the four remaining aspects as well.

Seahorse Valley of the Mandelbrot set is actually a four-dimensional thing, which includes not only all its Julia sets, but the scenes in the Oblate, Parabolic, Elliptic and Rectangular directions, as well as the oblique scenes sliced at unimaginable four-dimensional angles.   I have included a short chart of the six mutually perpendicular planes of the Z²+C Julibrot:

     real(C) and imag(C) = Mandelbrot aspect
     real(Z) and imag(Z) = Julia aspect
     imag(C) and real(Z) = Oblate aspect
     real(C) and real(Z) = Parabolic aspect
     real(C) and imag(Z) = Elliptic aspect
     imag(C) and imag(Z) = Rectangular aspect

The names of the four additional aspects are my own invention.

The orientation of today's image is within 1/100 of one degree of the Julia orientation.   The tiny rotation is toward the Rectangular orientation.   The outer edge of the fractal is the familiar Julia set with a C-value of -0.75,0.   Cut the maxiter to 100 to see it.

The strange-looking stuff inside the familiar Julia set is a gross enlargement and distortion of the Mandelbrot aspect of Seahorse Valley.   As far as I know, this is the smallest deviation from the actual Julia orientation of Seahorse Valley that I have yet seen.

The familiar Julia set of Seahorse Valley calculates in a few seconds, but today's slight rotation raises the calculation time to over three hours.   The incredible increase in time is due to the stuff on the inside of the fractal, most of which has an iteration count in the millions, and also to the fact that the periodicity must be turned off for the image to generate properly.

The name "Seahorse Valley-01" is a catalog number, since I will be doing many more Seahorse-Valley images in the month to come.   Luckily, no more images will take anywhere near today's 3 hours to calculate.   The rating of a 6-1/2 implies that I feel there is too much mathematical interest and too little artistic worth in the image.   Also, I have posted several images very similar to today's in the past, though the images were nowhere near as extreme.

Those with a few hours to spare may see the image by starting the included parameter file and coming back several hours later.   Those with more pressing things to do may see the finished image on the FOTD web site at:
Another perfect day prevailed here at Fractal Central on Sunday, with sunny skies and a temperature of 77F 25C.   The fractal cats spent most of the day in the side window, watching the other cats in the neighborhood wander by.

My day was pleasant enough.   If all goes well, the next FOTD image will be posted in about 6 hours.   Until then, take care, and when does the beginning end?


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

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

Seahorse_Valley-01 { ; time=3:09:55.05-SF5 on P4-2000
  reset=2004 type=formula formulafile=basic.frm
  formulaname=SliceJulibrot4 passes=1 maxiter=3500000
  center-mag=0/0/0.862069 float=y inside=0 logmap=yes
  params=90/0/89.99/90/-0.75/0/0/0/2/0 symmetry=yaxis
  periodicity=none
  colors=000HazJczLezNgzPizRjzTkzVmzXnzZoz`qzbszduzf\
  wzhzzjzzlzznzzpzzrzztzzvzzxzzzzzzzzzvzzrzzmzzhzzcz\
  zZzOj_NibMidLifKihJhkIhmHhoGhqFgtEgvDgxCgzIfuOepTd\
  kZdfccaibXnbTi`Vd_X_YZVX__YZdZZi_Zn`ZsaZwbZtYRqUJn\
  QCpVKqZRrbYsgdtkkuorrmmpkinjdlh`jgXdi_ZjaTkcNmfHnh\
  Boj6pl7mk8jk8gj9ejAbjA_iBYiBVhCShDQhDNgEKgEIgILiLN\
  jOPkRRlUTmXWn_YoNfLcfZtfkp`lmWliQlfLlbGl_AlW5lT0lQ\
  6nOBpLGqJMsGRtEWvC`wFdqHgkJjfLm`OpVQsQSvKUyFTuKTqP\
  SmTSiYReaRafRZjPWhNTfLQdKNbIK`GIZEFXDCVB9T96R73P61\
  O76R8BU8GX9L_9QbAUeBZhBckChnCmqDrtDvvFruHotJksLhrN\
  dqPapRYoSVnUSmWPlYMk_JjaDicAhd7g`CeYHdULcRQbNUaKZ`\
  HcZDgYAlX6rW3xV0zU2xS3tR4pP5mO6jM7gL8eJAbIB_GCXFDU\
  DERCFOAGM9KPBORCSTDWWE_YFc_GgaHkdIofJshKvjLulOumQu\
  nTuoVupYuq_trbtsdttgtuitvltwnnxmiymczlczlczlczkczk\
  czjczjczjczkczlhzlmzmrzmvznzznzzozzpzzpzzqzzqzzrzz\
  rzzizz`zzSzzJzzBzzIzzOzzU }

frm:SliceJulibrot4   {; draws most 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=z^(p5)+c
  |z| <= 9 }

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