Difference between revisions of "Weak Self-Assembly"
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(Created page with "Essentially, weak self-assembly can be thought of as the creation (or "painting") of a pattern of tiles that are a subset of the tile set(usually taken to be a unique "color") on...") |
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==Definition== | ==Definition== | ||
| − | A set $X \in \mathbb{Z}^2$ | + | A set $X \in \mathbb{Z}^2$ ''weakly self-assembles'' if there exists |
a TAS ${\mathcal T} = (T, \sigma, \tau)$ and a set $B \subseteq T$ | a TAS ${\mathcal T} = (T, \sigma, \tau)$ and a set $B \subseteq T$ | ||
such that $\alpha^{-1}(B) = X$ holds for every terminal assembly | such that $\alpha^{-1}(B) = X$ holds for every terminal assembly | ||
Revision as of 21:00, 21 May 2013
Essentially, weak self-assembly can be thought of as the creation (or "painting") of a pattern of tiles that are a subset of the tile set(usually taken to be a unique "color") on a possibly larger ``canvas of un-colored tiles.
Definition
A set \(X \in \mathbb{Z}^2\) weakly self-assembles if there exists a TAS \({\mathcal T} = (T, \sigma, \tau)\) and a set \(B \subseteq T\) such that \(\alpha^{-1}(B) = X\) holds for every terminal assembly \(\alpha \in \termasm{T}\).
