Domain Colouring

Remco Bloemen

2015-08-26

Take r=log(1+|x|)r = \log\left({1 + \left\vert{x}\right\vert}\right) then

H=argzS=12(1+sin2πr)V=12(1+cos2πr) \begin{aligned} H = \arg z \\ S &= \frac 12 \left({1 + \sin 2 \mathrm \pi r}\right) \\ V &= \frac 12 \left({1 + \cos 2 \mathrm \pi r}\right) \end{aligned}