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Fractal of the Day
by Jim Muth
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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: 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@mindspring.com jimmuth@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\
ae`ecaiacm_eqYfSLm28sBAkJBdRDXZEQfGInHBtT_ydwpdqgd\
l_dgRdaIdXAdS9oL8yECtDFpCIlBLhAOd9R_8UW7XS6_O5bK4e\
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omqqprtrsutuvvwwxxxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzz_Ef_EhZDiZCkZBlYBnYAoY9qY9r_Ep`InaNlbRkcVi\
e_gfcfghdhlbipaeibabbYXbcQbZJcUDcP6cG0cL6eQCgVIi_O\
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tmdulculauk`ukcqbfmUiiLhhMggNgfOffOeePedQdcRdcRcbT\
caUbaVb`Wb`Ya_Za__aZ``Ya`Yc`Xd_Xe_Wf_WgYXgXXgWYgUY\
gTZgSZgRZgVacYd_`fXciTglQjnMmqJptFsvCqtForHmpJloLj\
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==================================
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