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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Before attempting to run the parameter file of today's image, notice that it has been drawn by an updated version of the MandelbrotBC formula, which I have named MandelbrotBC1. This new version is identical to the old version except that I have replaced the fixed <trunc> function with a variable function, and replaced the fixed bailout radius of 100 with a variable parameter entry. Since I've lost all track of those who worked on this formula, I have credited it to 'several Fractint users'. Today's image uses the <floor> function, which curiously enough draws exactly the same images as the <trunc> function. I have not yet tested the various trig functions, though hopefully they will draw some interesting if not quite correct variations. The variable bailout is useful mainly with negative-exponent fractals, which I have not yet worked with. I also see that a developer's version of Fractint with rudimentary true-color capability is available, though at the present time, one can only see the image on the screen, say 'wow', stare at the image a while, and then shut down their computer. It's a start, but before I switch the FOTD to a true-color version of Fractint, the program will need the ability to cycle and change the colors, to save the image in true-color with data intact, and also to save the true-color image as a parameter file. And there's also the possibility that my stripped-down computer, used only for finding fractals, will not be able to display true-color with its meager 1 meg of video memory. But that's a problem I'll concern myself with if and when it arises. Today's fractal is quite decorative, an attribute that inspired the name "Decorative Minibrot". The irrational number entered as the real(p1) parameter may appear familiar. Actually, it is familiar. It is the square root of 3, a number I entered hoping to create midgets with 3-way symmetry. As of yet, I have found no such midgets, though I did find today's midget, which bears a curiously close resemblance to a standard quadratic midget. Only the chopped-off main bud reveals the midget's true nature. The parameter file is unusually fast, rendering in under two minutes. Of course, the download, which may be found at: The fractal weather today was clear as a crystal, with a temperature of 77F (25C), conditions that Thomas and Tippy, the fractal cats, consider ideal. Since they were deprived yesterday of their rightful time outdoors, I treated them to all the outdoor time they wanted today. My only concern is about a fox that has been seen lately in the neighborhood. The cats haven't confronted it yet, and I have no idea of what might happen if they meet. But right now, the dynamic duo are sleeping in their beds, a sign that it's time for me to shut down the fractal shoppe and call it a night. Until next time, take care, and if true-color is true, does that mean that 256-color is false? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
DecorativeMinibrot { ; time=0:01:52.60--SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=mandelbrotbc1 function=floor passes=1
center-mag=-0.73763/0.15494/2498.371/1/-124.999
params=1.732050807569/0/28.4/0 float=y maxiter=1000
inside=0 logmap=36 periodicity=10
colors=000mA9jBPnCHqDHtFDwGAzH5zH2zM4zS5zW7za8zeAz\
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sccpchycfzcfzc_zeUzfMzhHyiKsjMmlO0m02o04p27r3Bs4Du\
5Hv8KwAMyBQzCUzFYzG_zHbzIZzFWzBSz8Pz4Lz1Iz0Fz0Cz0A\
z0Dz2HzGKzUFzLAzD4z57zB8zFBzICzMFzOHzPKzPMzQPzQSzS\
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DlzFWzHWzHVzIVzIVzKUzKbzY
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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