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Self-Similar Fractal Tilings

Mark McClure
Organization: University of North Carolina at Asheville

2006 Wolfram Technology Conference
Conference location

Champaign IL

A self-similar tile is a two-dimensional set that satisfies a scaling identity. A square, for example, may be covered by four scaled copies of itself; this allows us to generate a tiling of the plane by squares. In this talk, we discuss the generation of such images paying particular attention to the boundary of the set. It turns out that the boundary frequently exhibits a fractal structure that may be analyzed using a generalization of self-similarity called digraph self-similarity. This allows us to compute the dimension of the boundary and to generate beautiful images efficiently.