Phase Plots of Complex Functions

Routines for creating color representations of complex functions (phase plots)

The ZIP-file provides several routines for creating color representations of complex (in particular analytic and meromorphic) functions.

Basically the argument (phase) of the function is encoded by a circular (hsv) color scheme and displayed directly on the domain of the function. The phase plot depicts clearly the location of zeros, poles, saddle points (zeros of the derivative), and essential singularities. Several modifications of the color scheme allow to incorporate additional information, like the modulus of the function.

The user must provide a field (matrix) of complex numbers z which covers the domain (typically a rectangle, a disk or an annulus) of the function, and a field of the same size with the corresponding values w=f(z). Then call

PhasePlot(z,w);

to create a phase plot of f on the domain of z. Try PPDemo to see a number of examples with different color options.

Version 2.3 comes with a graphical user interface (by Frank Martin) which allows easy control of color options (including coloring according to the NIST standard) and other parameters.

The screenshot shows a phase plot of a so-called atomic singular inner function, which has five essential singularities sitting at the fifth roots of unity.

For further information and a gallery of phase plots visit www.visual.wegert.com