A hyperbolic helicoid with torsion τ. The colormap is simply the parameter *v*.

The surface is defined by the parametric equations

\[ \begin{align} x &= \frac{ \sinh v \cos \tau u }{ 1 + \cosh u \cosh v } \\ y &= \frac{ \sinh v \sin \tau u }{ 1 + \cosh u \cosh v }\\ z &= \frac{ \cosh v \sinh u }{ 1 + \cosh u \cosh v } \end{align} \]Complete code for this example: