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Plenary Talk (Saturday Evening)

"The Art of Computation: M.C. Escher in the 21^st Century"

      Ellen Gethner
      University of Colorado
     (joint work with M.C. Escher, David Kirkpatrick, Steve Ogden, and Nick Pippenger)

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Abstract:
At the heart of the ideas of the work of Dutch graphic artist M.C. Escher is the idea of automation. We consider one such problem that was inspired by some of his earlier and lesser known work. We

pose an existence question in the realm of geometry,
solve the existence question by way of an efficient algorithm,
allude to a complete characterization, and
give a demonstration of an (interactive) implementation of our algorithm.

For the experts: The secret of each design is encoded by either one or infinitely many (number theoretic) lattices; we will allude to how we characterize all legitimate lattices by using techniques from graph theory and graph algorithms. From a certain point of view, the prototiles that we construct are canonical. We begin an analysis of the canonical prototiles by making a connection from lattices to binary quadratic forms to class number.
Gethner Picture