Currently I am working on some code to be able to draw hyperbolic geometry. I can already do some stuff. For example in this picture there are two sets of paralel lines. I use the Poincare disk model. In this model every line is a circular arc that is orthogonal to the outer circle. (https://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model)
The long term plan is to draw hyperbolic tessellations.