Self-Assembly of Infinite Structures

TL;DR

This paper reviews recent advances in the self-assembly of infinite structures within the Tile Assembly Model, highlighting impossibility results, novel systems, and open questions in the field.

Contribution

It provides a comprehensive review of recent results, including new tile assembly systems and theoretical impossibility proofs, advancing understanding of infinite structure self-assembly.

Findings

Identification of key impossibility results

Introduction of novel tile assembly systems for computational shapes

Presentation of open questions in the field

Abstract

We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent various notions of computation self-assemble. Several open questions are also presented and motivated.