Phase Plots of Complex Functions: a Journey in Illustration

Details Phase Plots of Complex Functions: a Journey in Illustration Phase Plots of Complex Functions: a Journey in Illustration

2010-07-14

arxiv.org/abs/1007.2295v1

Mathematics

Complex Variables

17 pages, 25 figures, to appear in Notices of the AMS

Scientific paper

We propose to visualize complex (meromorphic) functions $f$ by their phase $P_f:=f/|f|$. Color--coding the points on the unit circle converts the function $P_f$ to an image (the phase plot of $f$), which represents the function directly on its domain. We discuss how special properties of $f$ are reflected by their phase plots and indicate several applications. In particular we reformulate a universality theorem for Riemann's Zeta function in the language of phase plots.

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