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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's merely average fractal was found in the parent fractal that results when the formula Z^(2+0.01i)+C is iterated two levels up the logarithmic ladder. This parent at first appears to be a normal Mandelbrot set rotated so that its main spike faces southeast. But the surface appearance is deceiving. There is a split on the positive X-axis and the period-5 bud normally on the southwest shore of the main bay lies right on this split. It should come as no surprise that the features in the vicinity of the split are distorted. The minibrot in the center of today's image is a typical example. It appears to have gotten its north and south halves out of phase, with the two branches of Seahorse Valley no longer lining up. I named the image "Imaginary Wilderness" because fractals with complex and imaginary exponents are virtually unexplored -- at least by me. The rating of a 5 seems fair for a fractal done in such haste. The calculation time of just under 3 minutes may be avoided by going to the FOTD web site at: The sun was bright here at Fractal Central at sunrise on Saturday morning, but the temperature of 21F -6C promised a cold day. The fractal cats slept until it warmed to above freezing. My day turned busier than expected when I let F.L. talk me into a trip to a local antique mall to see the stuff that someone else threw away. (Actually, I kind of enjoyed it.) When we returned around sunset however, the cats were sulky at having been left alone for most of the day. The next FOTD will be posted in 24 hours, for all it is worth. Until then, take care, and search for the secret. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
ImaginaryWildernes { ; time=0:02:54.25-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC3 function=ident logmap=203
center-mag=+0.8488258557/-0.0209973644/15601.18/1/\
82.5/-3.5510218377e-010 maxiter=5000 periodicity=10
params=2/0.01/2/0 float=y passes=1 inside=0
colors=0008FA9FCAGDAGEAHEAHFAIFBIGBJGBJHBKHBKICKJC\
LJCLKCMKCMLDNLDNMDOMDONDPNEPOEPPEQPEQQERQFRRFSRFSS\
FTSFTTFTTFTTLYWRbZYh`cmcirfowhlsgjpfhmefiddfcbcb``\
aZX`XU_VRZTOYRKXPHWNEVJATLBUNCVODWQEWRFXTGYVHZWIZY\
J_ZK``LaaMacNbeOcfPchQdiRekSflTfnUgpVhqWisXitYjvZk\
xYlwZkvZkuZktZjsZjsZjrZiqZipZioZhnZhnZhmZglZgk_gj_\
fj_fi_fh_eg_ef_ee_de_dd_dc_cb_ca_ca_ca_ca_ca_cb`ac\
a_dbYecWfdUgeSgfQggOfgMffKffIeeGedEddCdcAdc8cb6ca6\
ca6b`6b`5a_5a_5aZ5`Y4`Y4`X4_X3_W3ZV3ZV3ZU2YU2YT2_U\
0YT2XS4VS5UR7TR8RQAQQCPPDNPFMOGKOIJNJIMLGMNFLOELQC\
KRBKT9JV8JW7IY5IZ4H`0Gb3Ha5Ia7J`9J`CK_EL_GMZIMZLNY\
NOYPPYRPXUQXWRWYSW_SVbTVdUUfVUiUUhVWgVYfV_eVadVccW\
ebWgbWiaWk`Wm_XoZXqYXsXXuWXwVYyWXzXWzXVzYVzYUzZTzZ\
Sz_Sz`Rz`QzaPzaPzbOzbNzcMzcNzdOzePzeQzfRzfSzgTzgUz\
hUziUziUzjUzjUzkUzkUzlUzmUzlUzmUzmUzmUzmUzmUzmUzmU\
zmUzmUzmUzmUzmUzmUzmUzmUz }
frm:MandelbrotBC3 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)+PI-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END PARAMETER FILE=========================================
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times.
