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arXiv · 2402.16284

Self-Assembly of Patterns in the abstract Tile Assembly Model

Phillip Drake·Matthew J. Patitz·Scott M. Summers·Tyler Tracy
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Abstract

In the abstract Tile Assembly Model, self-assembling systems consisting of tiles of different colors can form structures on which colored patterns are ``painted.'' We explore the complexity, in terms of the numbers of unique tile types required, of assembling various patterns. We first demonstrate how to efficiently self-assemble a set of simple patterns, then show tight bounds on the tile type complexity of self-assembling 2-colored patterns on the surfaces of square assemblies. Finally, we demonstrate an exponential gap in tile type complexity of self-assembling an infinite series of patterns between systems restricted to one plane versus those allowed two planes.

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Phillip Drake, Matthew J. Patitz, Scott M. Summers, Tyler Tracy. 2024-02-26. Self-Assembly of Patterns in the abstract Tile Assembly Model. https://arxiv.org/abs/2402.16284

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