Escherization

This paper introduces and presents a solution to the “Escherization” problem: given a closed figure in the plane, find a new closed figure that is similar to the original and tiles the plane. Our solution works by using a simulated annealer to optimize over a parameterization of the “isohedral” tilings, a class of tilings that is flexible enough to encompass nearly all of Escher’s own tilings, and yet simple enough to be encoded and explored by a computer. We also describe a representation for isohedral tilings that allows for highly interactive viewing and rendering. We demonstrate the use of these tools—along with several additional techniques for adding decorations to tilings—with a variety of original ornamental designs. CR Categories: I.3.5 [Computational Geometry and Object Modeling]: Geometric algorithms, languages and systems; I.3.8 [Computer Graphics]: Applications; J.5 [Arts and Humanities]: Fine arts; J.6 [Computer-Aided Engineering]: Computer-aided design...

• Type: Conference
• Year: 2000
• Where: SIGGRAPH
• Authors: Craig S. Kaplan, David Salesin
• Keywords: Closed figure, Computer Graphics, Isohedral Tilings, Original Ornamental Designs, SIGGRAPH 2000