Difference between revisions of "Weak Self-Assembly"
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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 | ||
| − | $\alpha \in \ | + | $\alpha \in \mathcal{T}_{\Box}$. |
==See also== | ==See also== | ||
Latest revision as of 11:42, 26 June 2024
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 \(\alpha \in \mathcal{T}_{\Box}\).
