The math is based on Moebius transformations in complex plane. They are genuine 3D hyperbolic transformation in 3D hyperbolic space but observed on the boundary of the Poincare ball (analog of Poincare disk for 3D hyperbolic space). The boundary of Poincare ball is projected onto plane via stereographic projection. So all the fishes are identical as they are in original Poincare disc view in M.C.Escher woodcut.
I had thought it was circles intersecting the rectangle boundary at 90 degrees, somewhat like a poincare disk. But the big "circles" in the lower right and upper left look decidedly elliptical.
Some form of credit would be appreciated
They are genuine 3D hyperbolic transformation in 3D hyperbolic space but
observed on the boundary of the Poincare ball (analog of Poincare disk
for 3D hyperbolic space). The boundary of Poincare ball is projected
onto plane via stereographic projection.
So all the fishes are identical as they are in original Poincare disc view
in M.C.Escher woodcut.
I had thought it was circles intersecting the rectangle boundary at 90 degrees, somewhat like a poincare disk. But the big "circles" in the lower right and upper left look decidedly elliptical.