A non-periodic tiling is simply one that is not fixed by any non-trivial translation. Sometimes the term described – implicitly or explicitly – a tiling generated by an aperiodic set of prototiles.

We present a construction of a family of non-periodic tilings using elementary tools such as modular arithmetic and vector geometry. These tilings exhibit a distinct type of structural …

“Ch 3: Tiling”, Harriss, Schattschneider, & Senechal, Handbook of Discrete and Computational Geometry, 2018 Isohedral (tiling): A tiling whose symmetry group acts transitively on its tiles.

An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only non-periodic tilings. The most widely …

Oct 1, 2025 · Non-periodic Tilings are unique because they do not repeat themselves in a regular pattern, even if you keep going infinitely. One reason people study non-periodic tilings is …

Oct 12, 2012 · Because of this only the hexagonal tiling is truly periodic whilst the triangular and square tilings are more properly described as non-periodic because they admit a potentially …

There are many examples of general polygons (not regular) that tile the plane, but in the most common cases they form periodic tiling. A periodic tiling is one where it is possible to make a …

Jul 2, 2024 · The random, spiral, and rep-tile tessellations are not periodic, because they have no translation symmetry. However, they are all made from tiles which can easily be rearranged to …

A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern (an aperiodic set of prototiles).

What makes these tiles special is that the resulting tilings are necessarily non-periodic: it is not possible to create the tiling by taking some (potentially very large) section and repeating it over …