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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image takes us to the northeast shoreline of the main bay of the Mandelbrot set, where we examine the valley leading to the large period-4 bud there. This valley is centered at 0.25+0.5i, and the slope of the main bay at this point is 45 degrees, which makes it quite simple to examine the area from all kinds of strange four-dimensional directions. Today's view is halfway between the Parabolic and the Oblate directions. The tiny buds that line the edges of the valley do appear in the image, but they no longer appear as tiny empty circles. The circles have been stretched in one of their dimensions to infinity, and appear as parallel slits partially obscured by fractal debris. By changing the imag(p1) parameter, we can see many different views of the scene, all of which show the buds as slits. If imag(p1) is set at 180, the image is the same, but we are looking at it from the opposite direction. Some of these other views are quite interesting, though I had little time to investigate them. I might do so sometime in the future, but with today's image rating only a measly 3, I will be in no great rush. With a render time of almost 8 minutes, the image has an overall value of 39. I named the image "Gruesome-brot", not because it is horrifying to look at, but because it's not a very good example of fractal art. The completed GIF image is available on the FOTD web site at: It reached 91F 33C here at Fractal Central on Monday, a temperature that left the fractal cats with nothing to do but sleep. They passed the afternoon sleeping in the yard, dreaming whatever it is that cats dream. Their moods were good when the time came to come indoors, so I guess their day was satisfactory. Today is starting cooler, but still mild. We'll see how the duo takes things. I managed to trim half the grass yesterday. The second half will be finished sometime this afternoon. Until next FOTD, take care, and look for the best. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Gruesome-brot { ; time=0:07:45.55--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=multirot-XZ-YW-new passes=1 float=y
center-mag=-2.2204e-016/-0.00217442/11.20316/0.2086
params=-45/0/2/0/0/0/0.25/0.5 maxiter=32000
inside=0 logmap=6 symmetry=yaxis periodicity=10
colors=000ZZh__i``jaakablbcmcdndeoefpfgqehqegpdfod\
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zzXzzWzzWzzVzzUzzUzzTkzSz }
frm:multirot-XZ-YW-new {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p3, c=e*imag(pixel)+p4:
z=z^(p2)+c,
|z| <= 36 }
END 20.0 PAR-FORMULA FILE==================================
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