Construction of fixed points of certain substitution systems by interlacing arrays in 1 and 2 dimensions

TL;DR

This paper introduces a novel interlacing array method to construct fixed points of substitution systems in one and two dimensions, leading to new ways of generating complex aperiodic structures like the Robinson tiling.

Contribution

It presents an alternative approach using interlaced infinite words to generate fixed points, extending the method from one to two dimensions for complex tilings.

Findings

Successfully constructs fixed points via interlacing in 1D and 2D

Extends the method to produce the Robinson tiling

Provides a new perspective on substitution systems and aperiodic tilings

Abstract

This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form a new, more complex, infinite word. By considering particular limits of interlacings of words, fixed points of substitutions are generated. This method is then extended to two dimensions, where a structure equivalent to a well known aperiodic tiling (the Robinson tiling) is constructed.