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Author Topic: An alternate projection for complex numbers  (Read 940 times)
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matsoljare
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« on: January 25, 2010, 01:03:20 AM »

Since every compex number can be described by angle and distance, rather than real and imaginary value, have anyone tried visually rendering them this way? Letting the x dimension in the image represent the angle, and y the distance, instead of real and imaginary part....  afro
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Timeroot
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« Reply #1 on: January 25, 2010, 02:38:17 AM »

That can be done with the "Rectangular to Polar" and "Polar to Rectangular" transforms in dmj.uxf in UF.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
Tglad
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« Reply #2 on: January 25, 2010, 03:32:43 AM »

"have anyone tried visually rendering them this way? Letting the x dimension in the image represent the angle, and y the distance"

It isn't that interesting really, just an unwrapping of the mandelbrot (if that's what you're referring to), but the topology of the shape doesn't change. In fact most zooms will look almost identical, just rotated or scaled.
It might be interesting to add C as a vector in this (angle,radius) space, which would give a different fractal.
i.e. for every C = (angle, radius), iterate (Z^2) rotated by angle, expanded by radius
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Timeroot
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« Reply #3 on: January 25, 2010, 04:26:37 AM »

Tglad: I'd actually already implemented that several days ago under "Polar Addition" in ahm.ufm. It looks somewhat like a sun. *yawn*
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
matsoljare
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« Reply #4 on: January 25, 2010, 01:44:45 PM »

Can you show some picture examples?
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makc
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« Reply #5 on: January 25, 2010, 04:31:42 PM »

maybe this one instead?
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kram1032
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« Reply #6 on: January 25, 2010, 04:43:33 PM »

Rieman-Sphere was tested a bunch of times, afaik...
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