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

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.