Re: displaying images in the complex plane
- To: mathgroup at smc.vnet.net
- Subject: [mg45904] Re: displaying images in the complex plane
- From: AES/newspost <siegman at stanford.edu>
- Date: Thu, 29 Jan 2004 05:34:56 -0500 (EST)
- References: <email@example.com>
- Sender: owner-wri-mathgroup at wolfram.com
In article <bv831l$i9u$1 at smc.vnet.net>, Nathan Moore <nmoore at physics.umn.edu> wrote: > Does any body have a favorite way of showing images in the complex > plane? Suppose I want to represent the function Tan[z], where z = a + > bi, how would you display that image if you were trying to explain the > complex plane to your students? > > Nathan Moore > University of Minnesota Physics > Personally I'd probably generate four simultaneous 3D plots (i.e., f[z] over the z plane) showing Re[f], Im[f], Abs[f], and Arg[f] all plotted above the a,b plane (or maybe only the first two). Most important, I'd start out with all plots empty. Then I'd display the f[z] values *only* along (i.e., above) the a = Re[z] axis, doing this simultaneously in all four plots, and in color. (Each 3D plot would have only a single raised line, not a surface.) Then maybe I'd do the same along only the b = Im[z] axis (or, maybe shift the "display line" slightly from the a axis to have a small finite b value) (or maybe rotate the real axis to a small angle in the a,b plane). Then I'd gradually add more lines in the a,b plane. (I'd do this by generating a lot of plots in Mathematica, and either animating them, or exporting them into a QuickTime move, or printing them to a PDF file.) The vitally important thing would be start with simplest stuff, then gradually build up the complete plots, with possibility of backing up at any point.