Replication of arbitrary hole-free shapes via self-assembly with signal-passing tiles

TL;DR

This paper introduces a universal self-assembly tile set within the Signal-passing Tile Assembly Model capable of replicating any arbitrary hole-free 2D shape without multiple stages or scaling, advancing shape replication capabilities.

Contribution

The work presents the first universal STAM tile set for arbitrary hole-free shape replication, eliminating the need for multiple stages, bins, or shape scaling.

Findings

Successfully replicates arbitrary hole-free 2D shapes

Reduces complexity compared to previous models

Operates with constant signal passing per tile

Abstract

In this paper, we investigate the abilities of systems of self-assembling tiles which can each pass a constant number of signals to their immediate neighbors to create replicas of input shapes. Namely, we work within the Signal-passing Tile Assembly Model (STAM), and we provide a universal STAM tile set which is capable of creating unbounded numbers of assemblies of shapes identical to those of input assemblies. The shapes of the input assemblies can be arbitrary 2-dimensional hole-free shapes. This improves previous shape replication results in self-assembly that required models in which multiple assembly stages and/or bins were required, and the shapes which could be replicated were more constrained, as well as a previous version of this result that required input shapes to be represented at scale factor 2.