Domain coloring

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Domain coloring is a technique for visualizing functions of a complex variable. The term "domain coloring" was coined by Frank Farris. Frank Farris

1 Motivation
- 1.1 Insufficient dimensions
- 1.2 Visual Encoding of complex numbers
2 Example
3 References
4 External links

[edit] Motivation

[edit] Insufficient dimensions

A real function $f:\mathbb{R}\rightarrow{}\mathbb{R}$ (for example $f (x) = x 2$ ) can be graphed using two Cartesian coordinates on a plane.

A complex analytic function $g:\mathbb{C}\rightarrow{}\mathbb{C}$ of one variable lives in a space with four real dimensions, and therefore only two complex ones. One way of depicting holomorphic functions is with a Riemann surface

[edit] Visual Encoding of complex numbers

Given a complex number $z = r e i θ$ , the phase $θ$ is represented by hue, and the modulus $r = | z |$ is represented by either intensity or variations in intensity. The arrangement of hues is arbitrary.