Each four-celled animal tiles the plane

Each Four-Celled Animal Tiles the Plane

An algorithm for deciding if a polyomino tiles the plane

For polyominoes coded by their boundary word, we describe a quadratic O(n) algorithm in the boundary length n which improves the naive O(n) algorithm. Techniques used emanate from algorithmics, discrete geometry and combinatorics on words.

A Strongly Aperiodic Set of Tiles in the Hyperbolic Plane

We construct the first known example of a strongly aperiodic set of tiles in the hyperbolic plane. Such a set of tiles does admit a tiling, but admits no tiling with an infinite cyclic symmetry. This can also be regarded as a “regular production system” [5] that does admit bi-infinite orbits, but admits no periodic orbits.

Plane Tessellation With Musical Scale Tiles And Bidimensional Automatic Composition

We present a method for arranging the notes of certain musical scales (pentatonic, heptatonic, Blues Minor and Blues Major) in the plane by using the idea of plane tessellation with specially designed musical-scale tiles. The motivation of such a representation is described, as well as the mathematical analysis of the possibility of its realization. As a main application of the idea we introduc...

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