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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: We have another two-image FOTD today. The first image shows the local scene; the second image backs off far enough to reveal the entire almost-Julia set. Yes, we're almost there. Today's rotation takes us to within 3/4 degree of the Julia plane. At this angle the thickness of the brilliant Mandelbrot bridge has been increased to over 76 times its normal thickness. We see the straight edges of the bridge now becoming quite ragged and increasingly indistinct, but the increasingly well-developed spiral in the upper right corner is now fully formed. All spirals converge clockwise, except the brilliant blue spiral near the center, which to be different converges counter-clockwise. This first image is almost but not quite a Julia set. The second image of the day, which shows the entire fractal, reveals how the width of the bridge has increased until it fills almost the entire scene. Only the top 1/4 of the image and a tiny area near the bottom are not covered by the grossly enlarged projection of the lower valley of the period-4 northeast bud of the M-set. The first image renders in 3-1/2 minutes, the second in 23 seconds. For those who prefer their fractals pre-rendered, the rendered images are available on Usenet at: The fractal weather today was typical of this part of the world at this time of year. The partly sunny skies were fine, but the temperature of 41F (5C) was too chilly for the fractal cats. And it's now time to shutter the fractal shoppe and settle down for the evening. I'll return tomorrow with the next to last in the series of Mandelbrot to Julia rotations. Until then, take care, and I'd walk 100 kilometers to see a four-dimensional object that was not a projection into three dimensions. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
4d-09 { ; time=0:03:25.07 -- SF5 on a P200
reset=2000 type=formula formulafile=multirot.frm
formulaname=multirot-XY-ZW function=flip/ident
passes=t center-mag=-1.11022e-016/8.32667e-017/10.41\
667 params=89.25/90/0.36775/0/0.281/0.487 float=y
maxiter=3600 inside=0 logmap=yes periodicity=10
colors=000BAABWfCAACVfDAAEVfEAAFUfFAAGUfGAAHUfHAAITf\
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}
4D-09a { ; time=0:00:22.92 -- SF5 on a P200
reset=2000 type=formula formulafile=allinone.frm
formulaname=multirot-XY-ZW function=flip/ident
passes=t center-mag=-1.55431e-015/-0.36429/0.8757189
params=89.25/90/0.36775/0/0.281/0.4871 float=y
maxiter=3600 inside=0 logmap=yes
symmetry=none periodicity=10
colors=000BAABWfCAACVfDAAEVfEAAFUfFAAGUfGAAHUfHAAITf\
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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 20.0 PAR-FORMULA FILE==================================
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times.
