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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Who ever thought that twisted donuts could be found in a fractal? Certainly not me. I expect to find twisted donuts in a bakery. But something about today's image reminds me of twisted cinnamon donuts, so I named it "Twisted Donuts". Donuts are not the healthiest food available. I eat them because they taste good, and not to be healthy. Fractals on a computer screen are rather useless, but I enjoy them anyway, because they are fun and they supply the adventure that it is now both too late and too early to enjoy otherwise. Today's image is a scene near the tip of the main stem of the Mandelbrot set. But it is not really the Mandelbrot set we are examining; it is only a look-alike. The iterated expression is Z^2.0000000003+C, which produces a fractal virtually indistinguishable from the M-set, except along the negative stem, which is where today's image lies. A couple outzooms will reveal that the main stem, which at the angle of today's image runs northwest-southeast, has split into two, and that today's scene lies between the two. The area is filled with features never before seen (at least by me) in the M-set. It is this kind of thing that I was searching for in yesterday's simple image, but never found. I really could have spent a bit more time on the coloring, so the rating of a 7 seems justified. The render time of under 2 minutes is plenty fast, at least for those with Fractint-ready machines. Those with Fractint-deprived units can still see the image by downloading it from the FOTD web site at: The Monday high temperature of 91F 33C was a bit much for the fractal cats, who cut their outdoor time to under 30 minutes before asking to come inside. A lively thunder-shower came up at 7pm and sent Thomas scurrying for cover. Tippy braved the action on the window shelf. Today is starting almost as hot. I expect the cats will have a similar day. For me, the day promises to be just another one to be forgotten as soon as it has ended -- except for the trip to the local donut shop, that is. The day's FOTD will live on however. And the next in the endless series of FOTD images will appear in 24 hours. Until then, take care and be iterative, but don't eat too many donuts. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Twisted_Donuts { ; time=0:01:52.82--SF5 on a P200
reset=2004 type=formula formulafile=slices.frm
formulaname=MandelbrotVE-VP passes=1
center-mag=-1.99994352213414000/-0.000000000515175\
04/5.741663e+009/1/-50/-4.15090305853904606e-005
params=2.0000000003/0/0/0/0/0/2.01/0 float=y
maxiter=600 inside=0 periodicity=10
colors=000AA9EAEI9IM8NQ8RPNaP`kPnuLmrImoFllCli9kf6\
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`eWddaicgmbmqasrdqrfprhorkmrmlroksnnsmqtmttlwtlytk\
utjqtinthjthgnaaAI31C06B5 }
frm:MandelbrotVE-VP {; Jim Muth real(c),imag(c)
a=p1, z=p2, c=pixel+p3,
b=sqr(real(p4)):
z=z^(a)+c,
|z| < b }
END PARAMETER FILE=========================================
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times.
