Universal Shape Replication Via Self-Assembly With Signal-Passing Tiles

TL;DR

This paper introduces a universal shape replication system using the Signal-Passing Tile Assembly Model (STAM), enabling the construction of arbitrary 3D shapes without scaling or pre-encoded info, by leveraging signal-controlled deconstruction.

Contribution

It presents the first universal shape replication method in STAM, capable of replicating any 3D shape without scaling or prior encoding, and demonstrates the necessity of deconstruction for certain shapes.

Findings

First universal shape replication system in STAM.

Able to replicate arbitrary 3D shapes without scaling.

Shows deconstruction is necessary for some shapes.

Abstract

In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding actions of other glues via "signals". Specifically, the problem we investigate is "shape replication" wherein, given a set of input assemblies of arbitrary shape, a system must construct an arbitrary number of assemblies with the same shapes and, with the exception of size-bounded junk assemblies that result from the process, no others. We provide the first fully universal shape replication result, namely a single tile set capable of performing shape replication on arbitrary sets of any 3-dimensional shapes without requiring any scaling or pre-encoded information in the input assemblies. Our result requires the input assemblies to be composed of signal-passing tiles whose glues can be deactivated to allow deconstruction of those assemblies, which we also prove is necessary by showing that there are shapes whose geometry cannot be replicated without deconstruction. Additionally, we modularize our construction to create systems capable of creating binary encodings of arbitrary shapes, and building arbitrary shapes from their encodings. Because the STAM is capable of universal computation, this then allows for arbitrary programs to be run within an STAM system, using the shape encodings as input, so that any computable transformation can be performed on the shapes.