View source for Shape Replication Through Self-Assembly and RNase Enzymes

{{PaperTemplate
|date=2010/01/05
|abstract=We introduce the problem of shape replication in the Wang tile self-assembly model. Given an input shape, we consider the problem of designing a self-assembly system which will replicate that shape into either a specific number of copies, or an unbounded number of copies. Motivated by practical DNA implementations of Wang tiles, we consider a model in which tiles consisting of DNA or RNA can be dynamically added in a sequence of stages. We further permit the addition of RNase enzymes capable of disintegrating RNA tiles. Under this model, we show that arbitrary genus-0 shapes can be replicated infinitely many times using only $O(1)$ distinct tile types and $O(1)$ stages. Further, we show how to replicate precisely $n$ copies of a shape using $O(\log n)$ stages and $O(1)$ tile types.
|authors=Zachary Abel, Nadia Benbernou, Mirela Damian, Erik Demaine, Martin Demaine, Robin Flatland, Scott Kominers, Robert Schweller
|file=[[media:Replicate.pdf | Shape Replication Through Self-Assembly and RNase Enzymes.pdf]]
}}