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Complex-Visualize

A package for visualizing arbitrary complex functions. Implements the strategy of domain coloring on the Riemann sphere.

Authors: Ma. de los Angeles Sandoval-Romero and Antonio Hernández-Garduño.

Introduction

Domain coloring is a technique for constructing a tractable visual object of the graph of a complex function. The package complexVisualize.wl improves on existing domain coloring techniques by rendering a global picture on the Riemann sphere (the compactification of the complex plane). Additionally, the package allows dynamic visualization of families of Möbius transformations.

To learn more about this package and view some nice examples, refer to this article.

Quick reference

Requirements

Mathematica version 8.0 or newer

Installation instructions

  • Clone this repository
  • Use the menu "File > Install..." to install the package complexVisualize.wl found in the cloned directory.

Usage

  • In a Mathematica session, load the package with:

    <<complexVisualize.wl

  • To plot the function f(z):

    complexVisualize[f[z], z]

    For example, the identity function (which is useful to try as a first example) is visualized with

    complexVisualize[z, z]

  • To get further usage instructions, type

    ?complexVisualize