Craig S. Kaplan and David H. Salesin. Escherization. SIGGRAPH 2000, the 27th International Conference on Computer Graphics and Interactive Techniques. New Orleans, Louisiana, USA, 25-27 July 2000.


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.


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