Abstract art generated by Thue-Morse correlation functions

TL;DR

This paper explores the use of Thue-Morse autocorrelation functions to generate abstract art, illustrating the aperiodic structure of the sequence and its relation to quasicrystal modeling.

Contribution

It introduces a novel method of creating abstract art based on Thue-Morse autocorrelation functions, linking mathematical sequences to visual representations.

Findings

Generated art captures the aperiodic structure of Thue-Morse sequences.

Demonstrates the connection between mathematical autocorrelations and visual patterns.

Provides a new perspective on modeling quasicrystal structures visually.

Abstract

The Thue-Morse sequence is an aperiodically ordered infinite binary sequence. It is used as a one-dimensional way to model the structure of a quasicrystal. For example, taking autocorrelations of these sequences (roughly, measuring how similar a Thue-Morse sequence is to translates of itself) we can gain understanding of the diffraction patterns of quasicrystals. We generate abstract art images from these Thue-Morse autocorrelation functions, that capture the aperiodic structure of the Thue-Morse sequence in a compelling way.