Cohomology Fractals
David Bachman, Saul Schleimer, and Henry Segerman

Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture
Pages 175–182
Regular Papers

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.

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