The algorithmic beauty of plants
The algorithmic beauty of plants
Word Processing in Groups
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Computation: finite and infinite machines
Computation: finite and infinite machines
The domino problem of the hyperbolic plane is undecidable
Theoretical Computer Science
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
A hierarchical strongly aperiodic set of tiles in the hyperbolic plane
Theoretical Computer Science
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We discuss regular production systems as a tool for analyzing tilings in general. As an application we give necessary and sufficient conditions for a generic triangle to admit a tiling of and show that almost every triangle that admits a tiling is "weakly aperiodic". We pause for informal discussion of a variety of other applications, such as non-quasi-isometric maps between regular tilings, non-periodic Archimedean tilings, growth, and decidability. Most generally, regular production systems provide a model for the organized growth of surfaces along a front, subject to local rules.