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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I have just finished wading through a pile of images posted to one of the 'busy' fractal mailing lists to which I am subscribed. I found the images 'nice'. Now, I'm not sure what 'nice' means when used to describe a fractal, but I use the word when I can think of nothing else to say. In today's case, I was surprised that, even to myself, one of the biggest fractal addicts, the fractals posted to the 'busy' list eventually started to 'all look the same'. (As I also suspect my own recent fractal efforts posted to this list are starting to do.) A large number of the images posted to that 'busy' list are created with fractal generating program 'X'. In addition to its 'transforms', this program features the ability to pile on the layers until the memory limit of the machine is reached. I think it is the transforms and especially the layers that compromise my appreciation of such images. In the world of fractals, simplicity and frugality seem to create the most interesting images. Z^2+C creates a more interesting fractal than Z^32+C, and Z^(-2)+Z^3+(1/C) does better than Z^2+Z^3+Z^4+Z^5+Z^6....+(1/C). The same law of diminishing returns seems to come into action when the layers are piled on in an effort to be more 'artistic'. I am sometimes given the argument that the layers of a fractal are like the instruments of a symphony orchestra, working together in harmony to make a pleasing single unit. I find this argument unconvincing. Visual images are not the same as auditory images. We constantly hear different sounds overlapping and blending, but unless we are visually impaired or cross our eyes, we do not observe overlapping visual images. In fact, the brain goes out of its way to combine the slightly different input from the two eyes into a single image. Maybe I'm just an old fractal fogey, clinging to the old fractal ways and unwilling to accept the current 'progress' in the avant-garde world of 'fractal art'. Maybe I'm still mourning the passing of the days when the messages in the fractal world read something like 'look at what I just found at x,x in the Mandelbrot set!' But whatever the reason, I like my fractals plain and simple. Whatever, my fractal images will continue to consist of one layer and usually the basic 'equal-escape-time' coloring method. Today's average image, with its single layer, simple generating formula, and basic coloring method, is a typical example. I named it "A Dish of Salad" because that's what it reminds me of. Then, seeing its average worth, I rated it a 6. With a render time of just under 10 minutes on a P1 200mhz machine, the parameter file is somewhat slow. All slowness can be eliminated however by downloading the finished GIF file from: The weather Monday here at Fractal Central was of the ideal late-winter variety. Blue skies, warm sun, light winds, and a temperature of 48F 9C made the porch the perfect place to pass the afternoon. Being cats, the dynamic duo passed the afternoon lounging in the sun on the porch. I'm about ready to pass the day working, so until next FOTD, likely on the Ides of March, take care, and things are not quite as they appear. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
A_Dish_of_Salad { ; time=0:09:44.80--SF5 on a P233
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-0.09194295359727203/+0.118613976553465\
50/4.963097e+008/1/-95/-1.66362817186210821e-005
params=1/-0.95/-1/1.05/-0.05/0 float=y maxiter=1450
inside=0 logmap=192 colors=000TIjXDm_8pX7mU6jR6gO5\
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vX5t`5rd4ph3nl3lpApfGsXMvOxgdwe`vdYucVtbSs`Pr_MqZJ\
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rNIsMGtOEuPDvQBwR9xT8yU6zV4zW3zX4zV5zU5zT6zS6zR7zP\
8zO8zN9zM9zLAzJBzHCzF0zJ4zN8zQBzUFzXIz_MzcQzf }
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
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