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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image reverts back to version 4 of the DivideBrot series of formulas (formulae for the well-educated). I needed to go back to version-4 because it allows control over the bailout radius. Today's image uses a negative exponent of Z, and negative powers of Z create fractals that tend to evaporate at very large bailout radii, such as the one-million of the version 5 formula. The parent fractal is a variation of the Z^(-3)+C Mandeloid, with a Mandelbrot set lying in the sandy fractal stuff at its center. Today's scene is located in an elephant-trunk spiral in the East Valley of this Mandelbrot set. The sandy stuff filling this area of the parent has infested the entire image, rendering the typical East Valley pattern almost invisible. Only the broad but careful coloring makes the spiral pattern visible. I named the image "Sand Castles" after the overall sandy effect. I rated it at a 7 because . . . well, I think it's worth it. The calculation time of 2-2/3 minutes makes the job of running the included parameter file, if not a gale, at least a breeze. And I'm not blowing hot air when I say that the finished image is available on the FOTD web site at: Absolutely perfect weather conditions prevailed here at Fractal Central all day Thursday. The deep blue sky and total sun were made even more enjoyable by a temperature of 79F 26C and the low humidity. The fractal cats must have agreed, for they got into a minor squabble over who would sleep in the spot of sunlight on the living room floor. My day was satisfactory. Tomorrow should be the same. The next FOTD will appear in 24 hours. Until then, take care, and the world is what you make of it. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Sand_Castles { ; time=0:02:41.15-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot4 passes=1 float=y logmap=172
center-mag=+0.04014873876952896/-0.000578747776991\
23/1.679661e+008/1/177.5/0 inside=0 periodicity=10
params=-3/0.15/-90/0 maxiter=5000 mathtolerance=0.05/1
colors=020IQzIQzISzIUzIUzIWzIZyIZyI_yIavIdvIdtIftI\
htIhrIirnktwkzwnzmpzIpzIrzItzItzIwzIyzIyzIzzIzzMzz\
KzzIzzIzzGzzGzzEyzEyzCwzCtzAtzczzczz7wz7nz5kz5kz3i\
z3hw1hs1fq0do0dn0am0_l0_k0Zi0Wg0We0Uc0Sa0S_0QY0OW0\
OU0MU0KU0KU0IU0GU0GU0Ez0Cz0Cz0Bz09z0Bz09z09z09z09v\
07r07m07h07c05Z05U05R05O03M03K13I33G52C72A827A25C2\
3E25E25E25G25G27G27G27I27I27I28I28K28K28K2AK2AM2AM\
2AM2AO2CO2CO2CO2CQ2EQ2EQ2EQ2ES2ES2GS2GS2GU2GU2IU2I\
X2IX2IX2IX2KY2KY2KY2KY2M_2M_2M_2MX2UY2QY2O_2M_2Kb2\
Ib2Gb2Ed3Cd5Ae98eB7gC5gE3gG1jI0jK0lM0lO0nS0nU0nW0p\
Z0p_0ra0rd0tf0th0nr0pn0rk0ti0vh0yf0zd0zf0zh0zi0zk0\
zn0zp0zr0zt0zw0zy0zz0zw0zr0zn0zi0zf0zf0zf0zf0zf0zf\
0zf0zf0zf0zf0zf1zf1zf3zf5zf7zf7zf8zfAzfCzfGzfEzfCz\
fCzfAzfAzf8zf8zf7zf7zf5zf5zf3zf3zf1zf1zf0zf0zf0zf0\
zf1zf1zf1zf3zf3zf3zf5zf5zf5zf7zf7zf7zf8zf8zf8zfAzf\
AzfAzfCzfCzfCzfEzfEzfEzfG }
frm:DivideBrot4 { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1), d=real(p2)+100:
z=sqr(z)/(z^(-a)+b)+c
|z| < d }
END PARAMETER FILE=========================================
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times.
