Title: An alternate projection for complex numbers Post by: matsoljare 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.... O0
Title: Re: An alternate projection for complex numbers Post by: Timeroot 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.
Title: Re: An alternate projection for complex numbers Post by: Tglad 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 Title: Re: An alternate projection for complex numbers Post by: Timeroot 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*
Title: Re: An alternate projection for complex numbers Post by: matsoljare on January 25, 2010, 01:44:45 PM Can you show some picture examples?
Title: Re: An alternate projection for complex numbers Post by: makc on January 25, 2010, 04:31:42 PM maybe this one (http://en.wikipedia.org/wiki/Stereographic_projection) instead?
Title: Re: An alternate projection for complex numbers Post by: kram1032 on January 25, 2010, 04:43:33 PM Rieman-Sphere was tested a bunch of times, afaik... |