FOTD -- July 01, 2003 (Rating 6)
Fractal visionaries and enthusiasts:
Today we begin the seventh month, yet the exact mid-point of the
year does not arrive until noon tomorrow. In honor of these
un-astounding facts, I have created a fractal. I named the
fractal "Fractal of Light". When I gave the image this name
last evening, I did so for a definite reason. This morning,
that reason appears much less persuasive, but the name has
already been given, and it will remain.
The parent fractal was created with the MandelbrotMix3a formula,
which mixes together four different powers of Z, but requires
that the critical points be calculated by hand. In today's
case, Z^2, 1/Z, Z^3 and Z^4 were combined, and Z was initialized
to 3.5059....
The parent fractal, which has X-axis symmetry, is a Mandeloid
rotated 180 degrees, with a large triangular area of chaos
beyond its East (or in this case, its West) Valley. The East
Valley itself is split in half, with a very skeletal line of
disconnected elements strung down its open center. Today's
scene is located near the edge of one of the smaller elements
in this string.
Because of the skeletal nature of the entire East Valley area,
today's image consists mostly of inside areas that have been
made visible and given detail by the 'fmod' inside-fill option.
I have rated the image at a 6, which is the most common FOTD
rating.
Because it must calculate 4 different powers of Z at every
iteration, the M-Mix3a formula is rather slow. Today's image
takes a full 11 minutes to render on my machine. The wait can
be avoided by downloading the completed GIF image from:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
or from:
<http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
With a temperature of 91F 33C and lots of sun, Monday was
another good cat day here at Fractal Central. Showers prowled
the area in the evening, but none made it to Fractal Central.
The intrepid duo passed the afternoon sleeping on the porch and
sitting in the shade under the holly trees.
Today promises to be a slightly cooler repeat. This is good,
because old cats become quite settled in their ways, and prefer
good days. So until next FOTD, take care, and keep a good
fractal thing going.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START 20.0 PAR-FORMULA FILE================================
Fractal_of_Light { ; time=0:11:04.76--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix3a function=ident passes=1
center-mag=+1.224869498561344/-0.000190723153669/1\
997855/1/-5/-8.58104708817e-009 float=y params=0.2\
/2/-1/-1/0.1/3/-0.03/4/3.50592829665/0 maxiter=1200
inside=fmod proximity=0.5 periodicity=10
colors=000WgbVebVcbVacU`cUZcUXcUWcXUa_S_bQZeOXhMVj\
KUdPSZURUZQOcPIhODmN7rM2wL6uNAsPEqRIoSMmUQkWUiXYgZ\
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omqqprtrsutuvvwwxxxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzz_Ef_EhZDiZCkZBlYBnYAoY9qY9r_Ep`InaNlbRkcVi\
e_gfcfghdhlbipaeibabbYXbcQbZJcUDcP6cG0cL6eQCgVIi_O\
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caUbaVb`Wb`Ya_Za__aZ``Ya`Yc`Xd_Xe_Wf_WgYXgXXgWYgUY\
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mNhkQgiSehUcfWbdY`b`ZabY_dWYfUWhTVjWPeYKa_EXa9TaBS\
aCSaDRaERaGQaHQaIPaJPaKP73R73T73V73X73Z73`73a85`96\
`A7_B8_C9ZDAZXmaWlaWjbWhb }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END 20.0 PAR-FORMULA FILE==================================
