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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I do not consider today's fractal to be a classic, though it rates an exceptional 8. Classic fractals are those with the inside color set to 0, and the outside consisting of flat equal-iteration bands. Today's image has the inside color set to 0, sure enough, but the outside consists of fmod with a proximity of 1.8. I tried the new outside=fmod coloring option when the normal outside=iter fell flat and failed to deliver all that I felt the scene had in it. Today's fractal is one of those rare images where the passes=b algorithm runs the fastest, though the time saved over passes=g is only a few seconds. I still find passes=b the most fun to watch in action, though I rarely use it because of its normal slowness and the fact that it cannot be used with inside=0. The formula that drew the image is -1.5(1/Z)+0.5Z^(3)+(1/C). I named the picture "Royal Blue Fractal" when I saw the unusually brilliant blues throughout the scene. The draw time from the parameter file is a fast 2 minutes, and running the parameter file is the fastest way of viewing the image. Those who would rather not run the parameter file will find the GIF file posted in an hour or so to Paul's web site at: The fractal weather today here at Fractal Central was very changeable. A damp chilly morning suddenly gave way as a warm front passed in early afternoon to hazy sunshine and a temperature of 68F (20C). The fractal cats took full advantage of the spring-like conditions by spending all afternoon in the yard, searching for some green grass to chew on. Unfortunately for them, there is little green grass in mid-winter. And I'm now searching for a way to end this FOTD. I guess the best way is to end it the way I always have, by saying, "until next time, take care," and adding, "where is the fractosophy?" Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Royal_Blue_Fractal { ; time=0:02:10.09 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=b
center-mag=+0.663679273531236/+0.07484778936714/6.33\
8219e+010/1/-140.008/0.008 params=-1.5/-1/0.5/3/0/0
float=y maxiter=2400 inside=253 proximity=1.8
outside=fmod logmap=yes symmetry=none periodicity=10
colors=000IEwMKy<2>Y_zZXzZSzZOzZMz<2>_Az_7za3za0za0z\
a0zV0zO6wIDrHBkHAfHA_H8VF7O<2>F67K7BO7FU7J<3>k7Zo7bs\
EgwJkzOozUuzZyzczzgsujk<2>_rNSuFMw6Ez07z0Az0BzBDzKEz\
VFzcHznIzwHzuFzrEzoDzmBykAwi8vf8uc7sa6r_<2>2nS0mQ0kO\
EbZRUgcKrqDzrHusJouMjvOewS_yVV<2>zbF<2>yiFykFwmFwoFv\
rFvsFuvFuwFrrIqnJnjKmfMjbNiZOfVQeRRbNSaJUZFVYBXX7YU6\
_<3>M6eK6fI6gH6jE6kD6m<3>46rB8oHBnMEmRHj<3>kRcqUbiYg\
a_mVbqNevHgzEerBck8bc6aY3_R0ZJ0YD0X63aDAfJHkQMqVSvaZ\
zgczm_yoYsrUnsRgvNbyKYzBYz2Yz8evEkmImn<3>YnnVikScj\
<2>MQevz7jmHZUQOAYK8cH7jE7qA6w64z34z7NzBeuEvnIsgMq\
bQnYUkRYiMafHccBkSKrHSy4_z0gzAfuOeobejqcezcUziIznN\
FQVJFaM4gO0fI7eBJc4Xb0gVDkNRoFes7rwSoUmn0VKJD0_7AZ\
3SY0jY6QiB6uKIy<2>gqziozjny<3>oijqgfqfc<2>sRQsMMuH\
IuBDv68v24g3A<2>43Q03UUBc20s00s000A3vE8w
}
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
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times.
