Date: Oct 7, 2013 8:19 AM
Author: David Park
Subject: Re: plotting complex functions in (x,y,t) space
Michael,

It is rather difficult to understand what the form of your function is and

what the role of t is. Not understanding that, it is even more difficult to

understand why you are trying to plot it as you describe. Maybe you could

clarify the question.

I sell (for $50) a Mathematica Application, Presentations, which has rather

extensive facilities for plotting complex functions, mostly directly in

terms of a complex variable z. Among other things it has DomainColoring,

which is something like what you describe, along with various coloring

functions and the ability to specify your own coloring. For drawing paths in

the complex plane it has ComplexCurve (suggested by Murray Eisenberg) so,

for example, you could draw a logarithmic spiral by ComplexCurve[Exp[(0.1 +

3 I) t], {t, -12, 6}]. It also has the ability to handle finite numbered

multifunctions.

My feeling is that domain coloring at first sounds great, and makes great

art work, but is not so good at extracting precise information about a

complex function. For one thing, people do not have an intuitive feel for

the coloring functions - whatever they are. Multiple presentations with

dynamic numerical values is usually better. One method that I like is to

drag a single locator around the complex plane, perhaps with a background

showing modulus, and attach an arrow to the locator representing the complex

value at that point. In a sense this is a local 4-D display because the

plane provides two dimensions and the arrow provides two more. If you

combine this with dynamic display of the numerical values you can explore

the space and extract precise information. It even works for a

multi-function where you can smoothly transition from one branch to another.

David Park

djmpark@comcast.net

http://home.comcast.net/~djmpark/index.html

From: Michael B. Heaney [mailto:mheaney@alum.mit.edu]

Hi,

I'd like to plot, on [x,y,t] axes, a complex function F[x,y,t], with the

magnitude of F represented by opacity, and the phase of F represented by

color. Does anyone have suggestions on how best to do this?

Thanks,

Michael