Domain Colouring

\gdef\g#1{\left({#1}\right)} \gdef\norm#1{\left\vert{#1}\right\vert}

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}