Fixed Point and Aperiodic Tilings

An aperiodic tile set was first constructed by R. Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals). We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. G

• Type: Conference
• Year: 2008
• Where: DLT
• Authors: Bruno Durand, Andrei E. Romashchenko, Alexander Shen
• Keywords: Aperiodic Tile Sets, DLT 2008, Kleene's Fixed-point Construction, Neumann Self-reproducing Automata, Theoretical Computer Science