Bi-Co Math Colloquium with Laura Seaberg
Abstract: Given a contraction from a metric space to itself, the contraction mapping theorem from real analysis guarantees the function has a unique fixed point. A beautiful consequence is the construction of fractals as the fixed point of a particular contracting operator. Fractals, in addition to being inherently beautiful and a jumping-off point for mathematical inquiry, have shaped public understanding of mathematics in the last 50 years. We will examine some tools in dynamical systems that make the study of self-similarity tractable, with a particular eye in fractal tilings of the plane. Tools such as finite graphs, special algebraic integers, and maps of the unit interval provide us with concrete ways in.
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