Standards
I had an unfortunate laundry experience the other day (turns out that “permanent press” is more wishful thinking than truth in advertising). I decided to entertain myself while ironing by listening to Eric Clapton tear through some blues standards (if you have to iron, this definitely helps). This got me wondering: Are there any “standards” in fractal art? That is, if fractal art is likened to blues or jazz or popular music, are there any images that might be the equivalent of “I’m Your Hoochie Coochie Man,” or “Take Five,” or “Night and Day”?
It seems to me that a fractal art standard would be an image intimately familiar to anyone intimately familiar with fractal art and vaguely familiar to those with less connection to the art. It would include a relatively simple formula, to increase its popularity and ease of calculation with various coloring schemes. Coloring formulas might be like genres in the musical analogy. (Here, I’m thinking in the Ultra Fractal schema, but such an image must not be tied to a particular platform.) The zoom and parameters should be such that the image is generally recognizable, but they could be varied as part of the artist’s rendition of that image.
Immediately, the overall Mandelbrot set leaps to mind. Other candidates might be zooms into the West Midget and the Seahorse and Elephant Valleys, the Koch curve, the Hilbert curve, and Newton's Method for z4 = 1. Any others?
posted by Unknown at 12:55 AM
2 Comments:
I thought about this quite a bit when I was making up banners for the blog.
I think there's really only two or three. The plain mandelbrot you mentioned and also just about any spiral shape.
Maybe one or two julia variations on the plain mandelbrot, like the big "S" one and the sideway s taken from the points on the "neck" of the mandelbrot.
Koch curve, maybe. Beyond that I think the number of images multiplies so fast that I couldn't see any of them being a quickly identified or easily recognizable standard outside fractal circles.
I think outside of fractal circles the iconic fractal shapes would be anything that appears in common resources like an encyclopedia or math textbook. That's where ordinary folks probably get their first introduction to fractals.
8/30/2006 2:36 PM
I know using the sometimes cranky word verification passwords for posting comments can be annoying, but these visual checks do prevent spam-bots from swamping the blog with invasive, unwanted junk.
8/31/2006 6:51 PM
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