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Ever heard of the Penrose tiling of the plane, the Rauzy fractal or
the Kakutani sequence of partitions of the unit interval? In my talk I
will introduce these beautiful geometric constructions, all of which
are defined using simple substitution rules. We will inspect these
substitution rules and see how matrices and graphs can be used to
model them, and how powers of the matrices and paths on the graphs
relate to tiles in the tilings and partitions of a set. These ideas
and relations are simple but deep, and they will allow us to discover
and prove some surprising properties of these well known
constructions.
Pizza will be served.
Penrose tiling
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Substitution partitions
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