Domain Colouring

% Remco Bloemen % 2015-08-26

\renewcommand{\g}[1]{\left({#1}\right)} \newcommand{\norm}[1]{\left\vert{#1}\right\vert} \newcommand{\π}{\mathrm π}

Take $r = \log\g{1 + \norm x}$ then

$$ \begin{aligned} H = \arg z \\ S &= \frac 12 \g{1 + \sin 2 \π r} \\ V &= \frac 12 \g{1 + \cos 2 \π r} \end{aligned} $$

Remco Bloemen
Math & Engineering
https://2π.com