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June 7, 1997: Seahorse Valley Angle June 6 June 8 1997 FOTD Home

seahorse

Fractal visionaries:

Sometimes familiar things appear like new when seen from a new perspective.  Such is the case with today's fractal.  We all know and love Seahorse Valley, located at -0.75 0n the Mandelbrot X-axis.  It is one of the most prolific areas of the entire M-set.  We are also familiar with the Julia set associated with this point -- a symmetrical series of buds sprouting from buds.

But there are four other perpendicular planes through this area, and some of these are quite attractive.  Today's fractal is a view of Seahorse Valley sliced along the YZ axis of the four-dimensional Julibrot figure.  I realize that it looks nothing at all like Seahorse Valley, but that's because we're viewing it from an entirely new direction.

Tomorrow, I'll show another slice of this most interesting area of the Julibrot figure.  I have not yet found all slices, however.  I'm still working on the formulas that display some of the oblique slices.  A few directions have so far eluded me, but every failure brings me a bit closer to a complete mapping.

Jim Muth
jamth@mindspring.com


START PARAMETER-FORMULA FILE FOR 19.6======================

SeahorseValleyAngl { ; time=0:00:11.15-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=Man-YZ-XZ passes=1
  center-mag=-4.44089e-016/2.22045e-016/0.8503401
  params=0/0.75/0/0 float=y maxiter=100000
  bailout=100 inside=0 logmap=yes
  symmetry=xyaxis periodicity=10 sound=off
  colors=000gGEP0HR0KT0MV0OX0QZ1S`2Ub3Wd4Yf5_i6ak7cn\
  8eo9gsAisBkuCmwDowElvFhvIeuLduOcuRctUcuXcv_cwbdxee\
  yhfwkfvnfuofsnfrmgplgokgnkgljgkigebaZXXTQRMKMGDGID\
  FKEFLEENFDPFCRGCSGBUGAWH9YH9ZI8`I7_HBZGFYFJYFNXEQW\
  DUVCYUBaUBdSJYRQSQXLOcFNj8Mq2LoBKmKJjTIhaOeXVbSeYI\
  `_Np4ho6fn9dnBbmD`lGZkIXjKUiNSiPQhROgUMfWKXFgXGfYG\
  eYHdYIdZIcZJbZJa_K`_L__LZ`MY`NY`NXaOWaPVaPUbQTbQSb\
  RScSRcSQcTPdUOdUNdVMeVLeWLeXKfXJfYIpcyocvnbrnbomak\
  lahk`ej`ai_Zi_VhZSgZOfYLbcAbcAbbBcbBcbCcaCcaDcaDd`\
  Dd`Ed`Ed`Fe_Fe_Fe_GeZGeZHfZHfYIfYIaqPapPapOboObnOb\
  mObmNblNbkNcjNcjMciMchMcgMdgLdfLdeLddLddKecKebKeaK\
  eaJe`Je_JfZJfZIfYI3`85`97`99`AB_AE_BG_BI_CK_CM_DOZ\
  EQZESZFUZFXZGZZG`YHbYHdYIVyLWxLWzLXzLXzKYzKYzKZzK_\
  zK_zKzzKzzJzzJzzJzzJzzJzzJzzJzzIzzIzzIzzIzzYzzQzzN\
  zzMzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:Man-YZ-XZ {; Jim Muth
; 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 PARAMETER-FORMULA FILE FOR 19.6========================