Jason Bell, Department of Pure Mathematics, University of Waterloo
“A Cobham-theorem analogue for fractals.”
The notion of self-similarity is fundamental in the study of fractals. Motivated by results in computer science, we define, for each positive integer k > 2, the class of k-self-similar fractals. Roughly speaking, these are compact subsets of [0, 1]d in which one the self-similarity can be described in terms of scaling by a factor of 1/k. We’ll explain why many familiar fractals such as the Cantor set and the Sierpinski carpet fit into this framework. We’ll explain why if a fractal is both k- and l-self-similar for two multiplicatively independent positive integers k and l then it must be a finite union of polyhedra and we’ll explain the connection of this result to a result of Cobham from computer science. (This is joint with Boris Adamczewski)
MC 5479