hyperbolic_translation 001
The disk is one model of hyperbolic geometry and what you see is a family of polar coordinates around points on the real axis. The movement of “disks” is a visualization of hyperbolic translation.

function: z → (z+c)/(1+conj(c)*z)

Preimage: polar conformal grid.
Domain: 0.01 ≤ |z| ≤ 0.95 and -π ≤ arg(z) ≤ π
m33 rs
Stereographic Projection onto a sphere.