Complex Functions

Domain coloring: each point z in the complex plane is coloured by the argument (hue) and magnitude (brightness) of f(z).

Function f(z)

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Phase → colour

−π−π/20+π/2+π

Hue = arg f(z) ∈ (−π, π] mapped to [0°, 360°].
Brightness = log-modulated magnitude, so concentric rings mark |f(z)| = e^k.

Zeros appear where all colours converge inward. Poles appear where all colours radiate outward.

Möbius: (z − 1)/(z + 1)

z = 0 + 0i

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