On substitution tilings of the plane with n-fold rotational symmetry

TL;DR

This paper presents a computer-assisted method for creating planar substitution tilings with n-fold rotational symmetry, including a novel 11-fold symmetric tiling, expanding the known examples in the field.

Contribution

The paper introduces a new computational approach to generate substitution tilings with n-fold symmetry, including the first known 11-fold symmetric tiling.

Findings

Successfully constructed an 11-fold symmetric tiling.

Method generalizes previous hand-constructed tilings.

First known 11-fold symmetric substitution tiling.

Abstract

A method is described for constructing, with computer assistance, planar substitution tilings that have n-fold rotational symmetry. This method uses as prototiles the set of rhombs with angles that are integer multiples of pi/n, and includes various special cases that have already been constructed by hand for low values of n. An example constructed by this method for n = 11 is exhibited; this is the first substitution tiling with 11-fold symmetry appearing in the literature.