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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: <bv831l$i9u$1@smc.vnet.net>
• 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.