I wish we could show that, moving everything together while keeping their relative distances. The whole tesselation might be too computation-costly to move; maybe there are tricks to re-use the computation. I was actually looking for a "playground" for hyperbolic tesselations, like Mathigon for the Euclidean plane. Would that be something you'd like to try? Can JavaScript accept two-finger input from touch-screen, if we want to rotate a figure?