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July 19, 1997: Faces in the Night July 18 July 21 1997 FOTD Home

faces

Fractal visionaries:

Today's rather ominous fractal is a scene in some remote oblique or skew plane of the julibrot.  I'm not sure of its orientation because I'm still trying to master this perhaps too ambitious formula of mine.

When I began my Fractal of the day series, it was with the intention of showing what could be done with simple 3-line formulas, but now I see that my formulas are starting to look suspiciously like those long, complex formulas which I originally put down.

Today's formula is not quite as complex as it seems, however.  It has some awkward expressions that could be made simpler, but I'm having so much fun working with it that I just haven't gotten around to tightening it up.

The picture is part of the Z^2+(0.005*Z^-3) julibrot.  Adding such a tiny portion of the -3 power of Z to the iteration fills the interior of the figure with chaotic detail.  Taking the odd planes stretches the inner detail out into tortured threads such as we see in today's picture.

When I saw the image, I pictured a ghost rising from the depths, so I named the picture "Wraith".  The complete image has been posted to alt.binaries.pictures.fractals and alt.fractals.pictures, though since the image draws in only 3 minutes, it would probably be faster to draw it from the parameter file than to wait for it to download.

Tomorrow, I'll return to the odd planes of the Z^2+(0.2*Z^3) mandeloid.  In its XY direction, that figure is one of my favorites.  Surprisingly, its perturbed planes hold more of interest than its "true" slice.

Jim Muth
jamth@mindspring.com


START 19.6 FILE=============================================

Faces_in_the_Night { ; time=0:00:08.62-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=SkewPlanes passes=1 center-mag=0.08976\
  /0.069479/0.7473842 params=0.4/0.4/0.3/0/0.005/-3
  float=y maxiter=1200 inside=253 logmap=yes
  symmetry=none periodicity=10
  colors=000145566987EA8IC9MEAQGCUIEYKGaMIdNKhPMnQMs\
  PMvRMzSMzUMzUMzUMzTMvTMvTMuTMtSMtSMsSMrSMrSMqRLpRL\
  oRLoRLnQLmQLmQLlQLkPLkPLjPLjPLkRKkTKlVKlWJmYJm_Jna\
  JnbIndIofIohIpiHpkHllJhmLcmO_nQWoSSpUNpXJqZFr`Km_P\
  h_UdZZ_ZcVYhQYmMXrHXwCWqI_jOddUhY`mSfqLlvFrzFpxEnu\
  ElsEkpEinDgkDeiDcgCadC_bCZ_CXYBVVBTTJTORUJZUDfU8aW\
  FXYMS_TNb_IdeDfl8hs3jz5kx7kv8luAmsCmqEnoGonIolJpjL\
  qhNqfPreRrcTsaUt_WtYYuX_vVavTcwRdxQfxOhyMhvLhtKhqJ\
  hnIgkHgiGgfFgcEgaEgZDgWCgUBfRAfO9fL8fJ7fG6iEAlDEoB\
  IkEJgHKcKM_NNWQOSTPOWQKZSGaTCdUDbTF`TG_SIYSJWRKUQM\
  SQNRPPPPQNORLNTJNUIMWGMXELYCK_AK`9Jb7Jc5Id9KfCMgGO\
  iJPjNRlRTmUVnYXp`Zqd_sgatkcnhYgeTabNV_HPXCGQI8KO0E\
  U3DV6DX9CYCC_FB`HBbKAcNAeQ9fT9hW8iZ8ka7ld7ng6oi6ql\
  5ro5tr4uu4wx3xt5wq7wm8viAvfCubEuZGtWItSJsOLrKNrHPq\
  DRq9Sp6Up2Wo6ZnBanFdmKglOjkTmkXpjYphZpf_pd`pbap`bo\
  YcoWdoUeoSfoQgoOzozioKznN }

frm:SkewPlanes {; Jim Muth
;p1=(0,0)=YW, (0,1)=XW, (1,0)=XZ, (1,1)=YZ
;p2=parallel planes, p3=optional variable extra term
a=real(p1), b=flip(cos(asin(real(p1)))), d=a+b,
f=imag(p1), g=flip(cos(asin(imag(p1)))), h=f+g,
z=real(pixel)+flip(real(p2)),
c=flip(imag(pixel))+imag(p2):
z=(d*(sqr(z)))+(real(p3))*(z^(imag(p3)))+(h*c),
|z| <= 36 }

END 19.6 FILE===============================================