Kleinian Creatures from the 4th Dimension
Limit set of a Kleinian group acting on the boundary of hyperbolic 4 space.
- Medium Print on Metal
- Technique Shader
- Dimensions 20x30in
- Year 2023
Exhibitions
The Mathematics
The limit set of a Kleinian group is the fractal set of points its dynamics accumulate on. For groups acting on hyperbolic 3-space these live on the boundary sphere S², giving the familiar fractal-and-circle patterns of Schottky and Apollonian gaskets. Analogous objects live one dimension up: on S³, the boundary of hyperbolic 4-space. This piece renders one such limit set after stereographic projection to R³.
Technique
Rendered with the same program as Klein in Jade, but here the custom path tracer treats the material as translucent: light has a different probability of scattering at each step of a random walk through it, evoking a sea creature rather than carved stone.