Difference between revisions of "Strict Self-Assembly"
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==Definition== | ==Definition== | ||
A set $X$ ''strictly self-assembles'' if there is a TAS $\mathcal{T}$ for | A set $X$ ''strictly self-assembles'' if there is a TAS $\mathcal{T}$ for | ||
| − | which every assembly $\alpha \in \mathcal{A}_{\Box}[\mathcal{T}] | + | which every assembly $\alpha \in \mathcal{A}_{\Box}[\mathcal{T}]$ satisfies $\dom \alpha = |
| − | X$. The set $\mathcal{A}_{\Box}[\mathcal{T}] | + | X$. The set $\mathcal{A}_{\Box}[\mathcal{T}]$ is the set of all [[Assembly#Terminal Assembly | terminal assemblies]]. |
==See also== | ==See also== | ||
Latest revision as of 12:33, 26 June 2024
Essentially, strict self-assembly means that tiles are only placed in positions defined by the shape. Note that if \(X \in \mathbb{Z}^2\) strictly self-assembles, then \(X\) weakly self-assembles. (Just let the subset of the tile set equal the tile set.)
Definition
A set \(X\) strictly self-assembles if there is a TAS \(\mathcal{T}\) for which every assembly \(\alpha \in \mathcal{A}_{\Box}[\mathcal{T}]\) satisfies \(\dom \alpha = X\). The set \(\mathcal{A}_{\Box}[\mathcal{T}]\) is the set of all terminal assemblies.
