A computer search for planar substitution tilings with n-fold rotational symmetry

TL;DR

This paper presents a computer algorithm that searches for substitution tilings with n-fold rotational symmetry, discovering new rules with 7-fold symmetry at various inflation factors.

Contribution

The paper introduces a novel computer algorithm for finding substitution rules on triangle sets with angles as multiples of π/n, revealing new 7-fold symmetric tilings.

Findings

New substitution rules with 7-fold symmetry discovered

Multiple inflation factors identified for these tilings

Algorithm effectively finds symmetric tilings

Abstract

We describe a computer algorithm that searches for substitution rules on a set of triangles, the angles of which are all integer multiples of {\pi}/n. We find new substitution rules admitting 7-fold rotational symmetry at many different inflation factors.