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 us 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 toolsalong with several additional techniques for adding decorations to tilingswith a variety of original ornamental designs.
escher paper tilings use simulated annealing simulation optimization parameterization class flexibility computation representation interaction rendering demonstrate design tesselations tools morphing