Fractal visionaries and enthusiasts:

Today we have a scene very near the Julia set of Seahorse Valley of the (-Z)^(2.5)+C Mandeloid.   Actually, the image has been rotated 6 degrees from the Julia orientation toward the Oblate orientation.

Instead of being at -0.75 on the X-axis, the seahorse singularity in this Mandeloid lies near -0.760037363.   To see the pure Julia set, which is far less interesting, change real(p1) to zero and reduce the maxiter to 150 to save time.

The first thing I notice about the image is the open slit along the X-axis.   This is the area near the singularity between the north and south arms of the valley.

Next, I notice the many proto-peanut holes.   Most have only two lobes, but the two at the left end of the fractal appear to have developed four lobes, and the brilliant open area on the X-axis just left of center is certainly a peanut hole in the making.

Actually, I'm not sure that the image is mathematically correct.   The X-axis symmetry might be an artifact of the math routine.   To see the problem, set real(p1) to something like 0.0000000001.   The image still has X-axis symmetry.   Then set real(p1) to zero, and the right half of the resulting fractal totally changes.   Such a small parameter change cannot possibly make such a large change in the resulting image.   But real or an artifact, today's image rates a 7.

The calculation time of 2-1/2 minutes is quite reasonable even for the most fanatical rationalists.   And never forget that the finished image is available on the FOTD web site at:
Thursday started with rain here at Fractal Central, but just after noon the sky brightened and the rain ended.   One final sprinkle fell at 2pm, but after that the sun appeared and it was a fine day, with a temperature of 77F 25C.   After chasing away a couple unwanted stray cats with their fierce glares and mighty growls, the resident fractal cats spent the day sleeping and ignoring the weather.

My day was average.   It's not boring; it's peaceful.   The next FOTD will be posted in 24 hours.   Until then, take care, and be fractalish.


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

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

Seahorse_Valley-19  { ; time=0:02:27.18-SF5 on P4-2000
  reset=2004 type=formula formulafile=basic.frm
  formulaname=SliceJulibrotMin4 inside=0 maxiter=50000
  params=84/0/90/0/-0.760036373/0/0/0/2.5/0 logmap=yes
  center-mag=-0.056338/0/1.03 float=y periodicity=10
  colors=000hKdhLehMfhNghOihQjhRkhTmhVnhWphYqh_rh_th\
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  zzLzzPzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:SliceJulibrotMin4   {; 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=========================================