Shape Replication

Overview

Replication is the concept of having a tile assembly system that can take input shapes and create new instances of that shape using a constant sized tile set.

Replication Using RNAse

In a paper by Abel, Benbernou, Damian, Demaine, Demaine, Flatland, Kominers, and Schweller, it is shown that replication can be achieved using an RNase augmentation of the staged tile assembly model. The shapes that their methods are limited to are arbitrary genus 0 shapes with minimum features of at least 5. Their first result showed that shapes can be replicated precisely n times using O(log n) stages and a constant number of tile types. This result works by... Their second result showed that shapes can be replicated indefinitely using a constant number of stages and a constant number of tile types. This result works by...

Replication Using Signal Passing Tiles

In a paper by Hendricks, Patitz, and Rogers, it is shown that replication can be achieved in the signal-passing tile assembly model. This method of replication starts by creating a frame around the input shape, which, after the frame tiles have verified that the shape is completely covered, breaks off of the input assembly and exposes new glues for the replicated assembly to start growth from.