---
tag: Z3FCJZF6WK
kind: concept
name: Aperiodic set of prototiles
msc: [52C23, 52C20, 05B45]
sources:
  - url: https://en.wikipedia.org/wiki/Aperiodic_set_of_prototiles
same_as:
  wikidata: Q17002261
  wikipedia: Aperiodic set of prototiles
---

## Summary

An aperiodic set of prototiles is a finite set of shapes that can [[tile|GKJK293DXS]] the plane, but only in ways that never repeat.
No tiling by these shapes is [[periodic|WFRGSBFZGV]].
Such sets show that local rules can force global order without periodicity, a phenomenon related to quasicrystals.

## Explanations

### L1 human

Most shapes that tile the floor, such as squares, can be laid out in a repeating pattern.
An aperiodic set is a set of tiles that do cover the whole plane, but any covering by them is forced to be non-repeating.
The [[Penrose tiles|MBE83FTRBG]], two shapes with marked edges, are the best known example.
In 2023 a single tile with this property was found, which answered the [[einstein problem|F456KQGPFV]].