Fractal visionaries and enthusiasts:

Today's diversion takes us to a very familiar place -- Seahorse Valley of the Mandelbrot set.  But today we see it in a new light.  The view is oriented halfway between the Oblate and Rectangular directions, and also rotated one degree from the normal.

At this strange angle only part of the M-set can be seen, stretched over 50 times in the horizontal direction.  In today's image I unstretched the Mandelbrot part far enough to leave it only about 16 times its natural width.

The remnants of the Mandelbrot aspect of Seahorse Valley are found near the center of the frame, colored baby pink, much as a newly-born seahorse might be.  The rest of the pink stuff is the distorted M-set, with the western part of the main bay on the right and the eastern part of the large period-2 bud on the left.  The foreground stuff is lesser-iteration stuff, which I inaccurately call Julia stuff, since it is found in all planes, including the Mandelbrot.

The rating of a 7 seems about right.  I put some extra effort into the coloring, though not as much as the image could use.

The name "Seahorse in Distress" refers to the pink Mandelbrot part of the image, which, even after some unsquashing, still looks quite flattened.

I was a bit relieved when FL arrived back from Havre de Grace safe and unharmed just before noon on Monday.  I listened courteously to the tales of the big 2-day wedding festival.

The Monday weather conditions here at FC were near perfect, with lots of sun, a temperature of 81F 27C and low humidity.  The fractal cats must have been worried about FL's absence.  When they heard her car pull into the driveway, they leaped up and ran to the door to meet her.

The next FOTD will be posted in 24 hours.  Until then, take care, and listen to the music of the spheres.

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


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

SeahorseInDistress { ; time=0:01:42.16-SF5 on P4-2000
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=SliceJulibrot4 passes=1 float=y
  center-mag=0/0.002/2.9/0.3805/90/0 params=22/89/0/\
  89/-0.75/0/0/0/2/0 maxiter=5000 inside=0 logmap=yes
  symmetry=none periodicity=6
  colors=000AVfAUeAQdAQcAQbAQaBP`CO_DNZEMYGLXIKWKJUM\
  ISOGQQGMSEIXCDZA9a75c41e52f62g73h83i93k94lA4mB4nC5\
  oD5qD6rE6sF6tG7uH7vH7wK8wN8wQ8wT8wW8xZ8xa8xd8xg8xj\
  8wiCviFuiJthMshQrhTqgXqg_pgboffnfimfmlepketjewjezk\
  fwkgukgrkhpkhmkikkjhkjfkkckkalh_mfYodWqaUr_TtXRvTP\
  wUPwVPxWPwXQvYSuZUsZWpZYmZ_jZagZce_ec`gaai__kcZzcb\
  mcXzc`mcVzcZmcUzcZmcUzcZmcUzcZmcUzcZmcUzcZmcUzeZmg\
  UziZmkUzmZmmUzmZmmUzmZmmUzmZmmUzmZmmUzmZmmUzmZmmUz\
  mZmmUzmZmmUzmZmmUzmZmmUzmZmmUzmZmmUzmZmrKzqUmrKzrU\
  mrKzrZmuKzuZmuKzuZmwKzwZmwKzwUmzPzzUmzPzzcmzPzzcmz\
  PzzcmzPzzcmzPzzcmzPzzcmzPzzcmzPzzcmzZmzcmzZmzcmzZm\
  zcmzZmzcmzZmzcmzZmzcmzZmzcmz_nzenzezzezzezzezzezze\
  zzezzezzezzezzezzezzezzezzezzezzhzzhzzhzzhzzhzzhzz\
  hzzhzzhzzhzzhzzhzzhzzhzzhzzhzzmzzmzzmzzmzzmzzmzzmz\
  zmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzm\
  zzmzzmzzmzzmzzmzzmzzmzzmz }

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