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

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