```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 andwhat the role of t is. Not understanding that, it is even more difficult tounderstand why you are trying to plot it as you describe. Maybe you couldclarify the question.I sell (for \$50) a Mathematica Application, Presentations, which has ratherextensive facilities for plotting complex functions, mostly directly interms of a complex variable z. Among other things it has DomainColoring,which is something like what you describe, along with various coloringfunctions and the ability to specify your own coloring. For drawing paths inthe 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 numberedmultifunctions.My feeling is that domain coloring at first sounds great, and makes greatart work, but is not so good at extracting precise information about acomplex function. For one thing, people do not have an intuitive feel forthe coloring functions - whatever they are. Multiple presentations withdynamic numerical values is usually better. One method that I like is todrag a single locator around the complex plane, perhaps with a backgroundshowing modulus, and attach an arrow to the locator representing the complexvalue at that point. In a sense this is a local 4-D display because theplane provides two dimensions and the arrow provides two more. If youcombine this with dynamic display of the numerical values you can explorethe space and extract precise information. It even works for amulti-function where you can smoothly transition from one branch to another.David Parkdjmpark@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 themagnitude of F represented by opacity, and the phase of F represented bycolor. Does anyone have suggestions on how best to do this?Thanks,Michael
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