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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: It was a bad day Friday here at Fractal Central, with a broken air-conditioner and complaining customers. I finally got the work problems behind me in the evening, though it was nature that supplied the cool air. Unfortunately, the letter from the fracprogrammers list appeared with its 'you have been unsubscribed' notice at exactly the right moment to act as the target for the frustration that had been building all day. After my outburst, I settled down and found a fractal. I looked exactly where someone just beginning their exploration in the world of fractals might look -- along the main stem of the Mandelbrot set, deep in the East Valley of the large midget. I did make a slight change however -- I double rotated the scene 45 degrees before starting my exploration. Surprisingly, the rotation makes little difference in the image that appears on the screen, though the larger midget in whose East Valley it appears, as well as the appearance of the M-set itself, have been totally changed. I named the image "Fractals-101", since such images serve as an introduction to the world of fractals. The rating of a below-average 3 might be a bit harsh, but I'm disappointed with myself for blasting the list administrator, who is probably not responsible for sending the notice, and I feel I deserve no better a rating. There is certainly nothing lacking with the render time, which at less than 1-1/2 minutes is probably less time than it will take to download the completed GIF image from: Friday, with a temperature of 95F 35C, was very hot and humid here at Fractal Center, especially indoors when the cool air stopped working. In the evening, a spectacular but harmless rain and lightning storm arose and cooled things down to 70F 21C. The fractal cats spent the entire afternoon outdoors, lurking in the shade of the holly trees, and venturing inside only when the thunder began. They must have sensed my bad mood. Today promises to be much better. My mood can be only better. The next FOTD, which should also be better, will appear in 24 hours. Until then, take care, and hope for the best. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Fractals-101 { ; time=0:01:24.75--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=multirot-XY-ZW-new function=ident/flip
passes=1 center-mag=-2.47457594999916800/0/4.60569\
6e+007 params=-45/45/2/0/0/0/0/0 float=y
maxiter=1800 inside=0 logmap=274
symmetry=xaxis periodicity=10
colors=000eK0fK0gK0hK0iK0jK0kK0lK1kQAgWIc`R_fZWlgT\
qoUtmUvmUxoZzqczshzumzvmzwmzxmzymzzmzzVSbn9lkDciGV\
gKNeNEcQ6`O5YN4VL3TK3pfCqeIrdNsdTtcYuccvbhvbmYdi9e\
eE84rJhR9MyMAVB5AUz5FVbUQTMJJFD976fIBL95dcm8gu6Xf4\
MT2BExWdhOUUGKF8AYWIMLCBA6iqWNRGDDZBc6WleCa88P54C2\
BcGSjeENLLmNF`HAPB5C5Aw75U303j02V01F_rpNSkHL_BEO57\
CqkRc_KRODDC6cZyQNdDBKr_Y_OMICBSHLE8AN6PB3CySyzJzj\
EjV9VF4FgmeX`VMPLBCAfeeWVVLLLAAAdmnsldSOKVrCFR6N2w\
H1hB1U50FybJVJ9_N0RH0IB0950H8DC69846423cCzQ8eD4LkT\
7_L5OE3C714SZ2IN19BUIcF9K3lSF`SAOI5C9JlZ9OHMZuBHT_\
WhuUytuzaaeJJLqyx_dcIKKH`n8IPR9lKLjEHiMbOXWLgQJqKH\
MYBVc8cl5lw2tz0gRgYepOtyOJuVTq`bmflilveYqXKlP6gHI_\
KTTNcMQcYLmEM`AGP7BC4kC35q0x_0cI0KCusUmENKwBKUCCv8\
Eb4GJXIlOK_GMO8OCgQeTSSEUEFWM7_c5aU3cK1eAqgT_iJIk9\
Imw9oUNqNNseBuL5wA3z72z51z2PzPGzG8z8mzbPzJDzaczpQz\
ZDzH9zM6zG4zB2z5hzXjzPlzH }
frm:multirot-XY-ZW-new {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4:
z=z^(p2)+c,
|z| <= 36 }
END 20.0 PAR-FORMULA FILE==================================
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times.
