Work

Tiling by near coincidence

Year: 2026

Type: article

Abstract: Moiré patterns of twisted and scaled bilayers have recently emerged as a fertile source of quasiperiodic order in two-dimensional materials. Inspired by these systems, we introduce the for generating quasiperiodic tilings of the plane. The method is intuitive—admitting pairs of nearly coincident points from superimposed layers—yet rigorous, as it maps naturally to the well-established cut-and-project formalism. It reproduces classical tilings, including the Ammann-Beenker, the Niizeki-Gähler, and the square and hexagonal Fibonacci tilings, and also reveals new tilings that are unlikely to arise from conventional constructions. The near-coincidence method is algorithmically simple and already realized in a web-based application that generates tilings from specified layer parameters and coincidence conditions. Future extensions include trilayer systems, where preliminary results yield dodecagonal order with square layers, and very small twist angles, where the method may capture the giant moiré patterns of bilayer and trilayer graphene.

Source: Physical Review Research

DOI: 10.1103/xjzf-xxns

Authors: Meshy Ochana, Ron Lifshitz

Institution: Tel Aviv University

Language: English

Topic: Quasicrystal Structures and Properties

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funder: Israel Science Foundation