Sculptural forms from hyperbolic tessellations

Abstract

A toolbox of algorithmic techniques is presented for creating a variety of novel, visually engaging, sculptural forms that express a mathematical aesthetic embodied within a plausibly organic organization. Hyperbolic tessellations in the Poincare plane are transformed in several ways to three-dimensional networks of edges. Then these edge networks are thickened to solid struts with a simple robust "strut algorithm". By the use of different transformations and adjustable parameters in the algorithms, a variety of high-genus forms result. The techniques are robust enough to produce watertight boundary representations to be built with solid freeform fabrication equipment. The final physical sculptures satisfy the "coolness criterion," that passers by will pick them up and say "Wow, that's cool!"