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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With much shopping to get done before the day ends, I will have to make today's FOTD discussion a fast one. Today's image pictures an enigma. "How can it be like that?" I ask myself as I study the image, which combines both Julia and Mandelbrot features of the (-Z)^2.003+C Julibrot. The scene is located in the East Valley area of the large midget on the split-up main stem of its parent. The outer part of the image is in the shape of a slightly distorted typical-East-Valley Julia set. Since the direction of the slice is slightly rotated from the exact Julia orientation, this distortion is to be expected. But the outer almost-Julia set is filled with the grossly stretched and enlarged apparition of the East Valley of the Mandelbrot midget itself. I do not know how it can be like this. It is a mystery. How can one look through an open Julia set and see an enlarged part of the Mandelbrot set? I know well enough how the numbers work to create the four-dimensional whole, but to picture that four-dimensional whole is as impossible to me as knowing the future or changing the past. I can comprehend it; I cannot see it. This mystery, this enigma, is what keeps me fascinated with fractals. To be so close to visualizing, yet stopped by my natural limits is frustrating, but at the same time, fascinating. Reading the books written by others who share my frustration leads me to realize that the future is hopeless. Neither I nor anyone else shall visualize a four-dimensional object as it exists in its entirety in its own space at a single moment of time. And if anyone were to actually visualize something as simple as even a hypercube, that person could do no more than describe the arrangement of its parts -- a thing that we already know. The visualization would be impossible to communicate. I named today's image "The Blade". The distorted greenish object visible in the open area does resemble a blade. I rated the image at a 5, which is average. The render time of 3-3/4 minutes is also about average. And for those who would rather not render, the completed image can be found at: The rain arrived at 1pm on Friday, and fell steadily for the rest of the day. Despite the chilly temperature of 39F 4C, the fractal cats managed just enough outdoor time before the rain began to keep them happy until evening. This morning is once again threatening rain, and I can no longer put off the shopping that is unnecessary yet necessary at this time of year. But this evening, when the running around is behind me, I'll turn once again to fractals and the worlds that numbers create. Look for the next fractal in 24 hours. Until then, take care, and don't be too busy to enjoy the day. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
The_Blade { ; time=0:03:44.59--SF5 on a P200
reset=2002 type=formula formulafile=julibrot.frm
formulaname=SliceJB-new-min passes=1 center-mag=0.\
00501044/-0.000625978/8.912656/1/90/3.885780586188\
04789e-016 params=0.487/0.488/0.508/0.511/2.003/0/\
-1.74714/0/0/0 float=y maxiter=3000 inside=0
logmap=yes symmetry=none periodicity=10
colors=000VKlTJmRIoQHpOGrMFsLEtECY8ACBCEDEGFFIHHKK\
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zz9zzAzzAzzAzzAzzBzzBzzBzzBzzBzzDzzFzzHzzJzzLzzNzz\
PzzRzzTzzQzzOzzMzzKzzHzzF }
frm:SliceJB-new-min {; thanks to John Goering, July 1999
pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1),
b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), ca=cos(a),
cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d),
sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg,
s=v*sin(a), c=p+flip(q)+(p4), z=r+flip(s)+(p5):
z=(-z)^(p3)+c
|z|<=100 }
END 20.0 PAR-FORMULA FILE==================================
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