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

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