Fractal visionaries:

About eight years ago, when I saw the Mandelbrot set appear on my screen for the first time, the first area I examined was Seahorse Valley.  I don't think it had been given its name yet, but it was the most interesting area of the whole set.  Since that time, Seahorse Valley, located at -0.75, has been my favorite place to go when I wanted a good fractal with as little work as possible.

I never did find a seahorse as convincing as the elephants parading out of East Valley; I saw only their tails.  But that doesn't matter -- I'm sure the seahorses are there.  Otherwise, why would it have been named Seahorse Valley.

Today's fractal, which I named "Midnight" because of the somber colors, is an oblique slice of Seahorse Valley, best viewed in reduced light.  I won't even attempt to describe the orientation of the slice.  I can say only that it is near horizontal, but off to the side and tilted at something like a 10 degree angle.

These oblique planes of the M-set are filled throughout with swirling and stretching elements, much as in today's image.  But the rippling effect where the two prominent center elements skew off the plane of the screen is new to me.  Nothing like it appears anywhere in the classic Mandelbrot or Julia sets.

I'm becoming a bit hooked on the oblique slices of the Julibrot, which are virtually unexplored.  When that happens there's nothing to do but explore like crazy until my enthusiasm runs its course.  So bear with me if I post a few more oblique images.  I'll soon return to fancier fractals.

As is always the case, the finished image has been posted to a.b.p.f. and a.f.p. for convenience.

Jim Muth
jamth@mindspring.com


START COMBINED FILE FOR 19.6===============================

Waves_in_the_Night { ; time=0:02:19.78-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=Man-YZ-XZ passes=t center-mag=1.25579\
  /-0.144754/25.40284 params=0.16/0.75/0.1/0 float=y
  maxiter=14400 inside=253 logmap=10 periodicity=10
  colors=0008CC8BB8BB7AA7997986876866755745645635524\
  514404405515515626626636736746747857857967967968A7\
  8A78A88B88B99B99CA9CA9CA9DBADBAECAECAEDAFDBFEBFEBG\
  FBGFBGFCHGCHGCHHCIHCIIDJIDJJDJJDKKDKKEKKELLELLELME\
  MMFMNFMNFNOFNOGOPGOPGOPGPQGPQHPRHQRHQSHQSHRTIRTIRT\
  ISUISUISVJTVJTWJUWJUXJUXKVYKVYKVYKWZKWZLW_LX_LX`LX\
  `LYaMYaMZbMZbMZbM_cN_cN_dN`dN`eN`eOafOafOafObgObgP\
  chPchPciPdiPdjQdjQekQekQekPdiOdhOdgNceNcdMccMcbLba\
  Lb_KbZKbYJaXJaVIaUIaTH`SG`RG`PF`OF_NE_ME_LD_JDZICZ\
  HCZGBZEBYDAYCAYBBXCBXKBXKCXKCXKCXKCXKDXUDXUDXUDXUE\
  XUEXUEXUEXUFXUFXUFXUFXUGXUGXUGXUGXUHXcHXcHXcHXcIXc\
  IXcIXcIXcJXcJXcJXcJXcKXcKXcKXcKXcLXmLXmLXmLXmMXmMX\
  mMWmMWmNWmNWmNWmNWmOWmOWmOWmOWmPWmPWmPWmPWmQWmQWmQ\
  WmQWmRWmRWmRWmRWmSWmSWmSWmSWmTWmTWmTWmTWmUWmUWmUWm\
  UWmVWmVWmVWmVWmWWmWWmWWmWWmXWmXWmXWmUUmUUmUUmUUmUU\
  mUUmUUmUUmUUmUUmCDFUUmUUm }

frm:Man-YZ-XZ {; Jim Muth, Thanks to Benno
; p2 = 0 = Julibrot YZ plane
; p2 = 1 = Julibrot XZ plane
; p2 = >0 <1 = Oblique planes
z=real(pixel)+flip(real(p1)),
c=imag(pixel)+flip(imag(p1)),
a=p2, b=flip(cos(asin(p2))):
z=sqr(z)+((a+b)*c),
|z| <= 25 }

END COMBINED FILE FOR 19.6=================================