Function z → i tan

function: z → i*tan(i*z/2)

Preimage: rectangular grid.
Domain: -3.8 ≤ Re(z) ≤ 0 and 0 ≤ Im(z) ≤ 2*π

Stereographic Projection onto a sphere.

Pascal Code for TanH(Z) Map:

ConformalMappingFunction := 
     TangentH(RealTimesComplex(-0.5, z));

z_hyperbolic_tangent.pdf