Description

Breaking the perfect symmetry of a triangular tiling of the circle yields a spiral of deformed tilings, hinting at a deep connection between symmetry, rigidity and flexibility in mathematics.

Hyperbolic and real projective geometry are two mathematical spaces obeying different geometric rules than the familiar Euclidean plane.  This piece depicts a symmetric tiling of hyperbolic space (central circle tiled by green triangles), emphasizing its relationship to triangular tilings of convex domains in real projective space.
Real projective deformations of hyperbolic structures constitute an active field of mathematical research, but accurate visualizations are few and far between.  To produce this work, I used a computer algebra system to compute the relevant mathematical objects (certain discrete subgroups of SL(3,R)) and wrote custom graphics software in Mathematica render this algebraic data in its visual form.