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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I goofed. In yesterday's FOTD I stated that it would take 10^64 transfers to solve the Tower of Hanoi puzzle. Actually, it would take only 2^64 transfers. This means that time is running out faster than we thought. Today's image might be the cover of a cheap horror novel about a homicidal maniac, but it is actually an almost-Julia set of East Valley. The outer shape of the Julia set is there sure enough, and the symmetrically placed bubbles in the interior are as expected, but the intruding dagger certainly does not belong in such an otherwise serene image. That dagger inspired the name "A Stab in the Back". The rating of a 7 seems about right for the picture. Actually, the dagger is East Valley itself, hugely enlarged and rotated out of position. How can it be this way? For a hint, consider the hugely increased length of your shadow when the sun is setting. The shadow is stretched in one dimension by the oblique projection. But in four-dimensional space, an object's shadow may be stretched equally in two dimensions by projection, which amounts to enlargement. The formula is a new one with a variable escape radius, written specially for today's image. The bubbly effect was achieved by rendering the image with the inside set to 'bof61'. The outside consists of the usual equal-iteration bands. The extreme bailout of 25100 was necessary to give a few spare bands for the highlights on the bubbles. The slight horizontal stretching is just for effect. The render time of under 5 minutes will try no one's patience, unless they have more important things to do. But what could be more important than calculating a fractal never before seen? The unfortunate fans with SOTA units that crash when they hear the word 'Fractint' will find the finished image posted in GIF format on the FOTD web site at: Thursday started foggy here at New Fractal Central, but by 11am the fog burned off, leading to a perfect sunny afternoon with a temperature of 81F 27C. The New Fractal Cats were too busy romping with each other to notice the sun. They stopped misbehaving only when it was time to enjoy their evening treats. My day was busier than average, and the work will only get worse over the next few days. I'll try to keep the FOTD going during the rush, but there are no promises. The next FOTD might appear in 24 hours. (I'll give 50-50 odds of it appearing.) If it fails to show up, check for it the following day. Until next time, take care, and dimensions may be all in the mind, but in which dimension is the mind? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
A_Stab_in_the_Back { ; time=0:04:49.68--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=JulibrotZ-New passes=1 center-mag=0/0/\
0.8935863/1.0347 params=2/0/0.2501/0/0.0003/\
-0.0004/25000/0 float=y maxiter=10000 inside=bof60
logmap=yes periodicity=10
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frm:JulibrotZ-New {; Jim Muth
; Draws oblique slices of order n Julibrot Figure
; P1 defines power of Z, P2 determines center of slice
; P3 determines angle of slice
z=pixel, c=p2+(pixel*p3):
z=z^p1+c,
|z| < p4+100 }
END PARAMETER FILE=========================================
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times.
