Fractal of the Day
by Jim Muth
FOTD -- December 07, 1998
Fractal visionaries:
The incredible weather continued today here at Fractal Junction. Many temperatures around the area were all-time highs for December -- in the low 80's-F high 20's-C -- with backyard barbeques and sunbathers making it a Christmas season such as one would expect in Australia.
The fractal hunting was also hot, though not quite as hot as the temperature. The scene I found today is located in a perturbed part of the northern branch of Seahorse Valley of the classic M-set. The slice is double-rotated 61 degrees toward the Julia direction, which is a direction impossible to visualize in relation to the M-set.
I find the picture particularly fascinating, with its infinitely divided foreground Julia material standing out in stark contrast to the brilliant leftovers of the M-set in the background. To get this effect, I calculated the image with Fractint's ranges feature in effect, and colored it with one of my minimalist palettes. I named the picture "Obscured Radical" because it is a picture of a Mandelbrot radical partially obscured by the Julia material in the foreground. I believe the word "radical" is of Mr. Mandelbrot's own invention, and refers to the entire complex of features associated with a Mandelbrot bud.
The parameter file runs in less than an hour, but if this is still inconvenient, the GIF file of the finished 640x480 image has been posted to:alt.binaries.pictures.fractalsand to the W.W.W. at the following URL:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Tomorrow I'll return with another fractal and another few words. And don't give up on that wanabee philosophy -- I'm still working on it, and it might even be ready by tomorrow. Until then, take care, and as the wise old philosopher said, "a fractal a day keeps boredom away."
Jim Muth
jamth@mindspring.com
START FORMULA================================================
multirot-XY-ZW {; draws 6 planes and many 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))+p2,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3:
z=sqr(z)+c,
|z| <= 36 }
END FORMULA==================================================
START PARAMETER FILE=========================================
Obscured_Radical { ; 25min on 486-100mhz, 640x480
reset=1960 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW function=ident/flip
passes=t center-mag=-1.56858310350634000/+0.152260\
83477533180/460.2684/1/79.999 params=61/61/0/0/0/0
float=y maxiter=32767 bailout=25 inside=253
logmap=48 symmetry=xaxis periodicity=10
ranges=0/-1/600/615/635/665/700/750/900/1200/1800/35\
00/32767 colors=000A50UUZKQRPUVUTZZXbcWf<2>rhrwlv\
zuz050<238>050UGm050050
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Obscured_Radical { ; 25min on 486-100mhz, 640x480
reset=1960 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW function=ident/flip
passes=t center-mag=-1.56858310350634000/+0.152260\
83477533180/460.2684/1/79.999 params=61/61/0/0/0/0
float=y maxiter=32767 bailout=25 inside=253
logmap=48 symmetry=xaxis periodicity=10
ranges=0/-1/600/615/635/665/700/750/900/1200/1800/35\
00/32767 colors=000A50UUZKQRPUVUTZZXbcWf<2>rhrwlv\
zuz050<238>050UGm050050
}
frm:multirot-XY-ZW {; draws 6 planes and many 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))+p2,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3:
z=sqr(z)+c,
|z| <= 36 }
END 19.6 PARAMETER-FORMULA FILE==============================
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