Cohomology fractals

TL;DR

Cohomology fractals are novel visual representations derived from cohomology classes on hyperbolic three-manifolds, enabling real-time zooming and revealing complex geometric features.

Contribution

The paper introduces cohomology fractals, a new type of image associated with cohomology classes on hyperbolic 3-manifolds, with an implementation for real-time visualization.

Findings

Includes images made from circles and complex features

Allows zooming in any direction to arbitrary depth in real time

Related to limit sets of Kleinian groups but with key differences

Abstract

We introduce cohomology fractals; these are certain images associated to a cohomology class on a hyperbolic three-manifold. They include images made entirely from circles, and also images with no geometrically simple features. They are closely related to limit sets of kleinian groups, but have some key differences. As a consequence, we can zoom in almost any direction to arbitrary depth in real time. We present an implementation in the setting of ideal triangulations using ray-casting.