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Re: plotting complex functions in (x,y,t) space
Posted:
Oct 7, 2013 8:19 AM


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 4D 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 multifunction 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



