Difference between revisions of "Assembly"
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==Seed Assembly== | ==Seed Assembly== | ||
In a seeded tile assembly model, a seed assembly refers to the initial structure from which growth begins. | In a seeded tile assembly model, a seed assembly refers to the initial structure from which growth begins. | ||
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| + | ==Terminal Assembly== | ||
| + | Let $\mathcal{T} = (T, \sigma, \tau)$ be a TAS. An assembly $\alpha \in \mathcal{A}[\mathcal{T}]}$ is terminal, and we write $\alpha \in \mathcal{A}_{\Box}[\mathcal{T}]}$, if no tile can be $\tau$-stably added to it. It is clear that $\mathcal{A}_{\Box}[\mathcal{T}] \subset \mathcal{A}[\mathcal{T}]}$. Note that similar definitions of terminal assembly hold for other tile assembly models such as the 2HAM and derivatives of the 2HAM and aTAM. | ||
[[Category: Terminology]] | [[Category: Terminology]] | ||
Revision as of 16:02, 21 May 2013
Contents
Informal Description
An assembly generally refers to the structure created from tiles binding together.
Definition
An assembly in \(n\)-dimensional space (most commonly taken to be \(n=2\) or \(n=3\)) is a partial function \({\alpha}:{\mathbb{Z}^n} \dashrightarrow {T}\).
Tau-stable Assembly
An assembly is \(\tau\)-stable if it cannot be broken up into smaller assemblies without breaking bonds of total strength at least \(\tau\) for some \(\tau \in \mathbb{N}\). For example, in models such as the Abstract Tile Assembly Model (aTAM) and the Two-Handed Assembly Model (2HAM) all assemblies are \(\tau\) stable where \(\tau\) is the Temperature of the system, but in models such as the Kinetic Tile Assembly Model (kTAM) there can exist an assembly that is not \(\tau\)-stable.
Seed Assembly
In a seeded tile assembly model, a seed assembly refers to the initial structure from which growth begins.
Terminal Assembly
Let \(\mathcal{T} = (T, \sigma, \tau)\) be a TAS. An assembly \(\alpha \in \mathcal{A}[\mathcal{T}]}\) is terminal, and we write \(\alpha \in \mathcal{A}_{\Box}[\mathcal{T}]}\), if no tile can be \(\tau\)-stably added to it. It is clear that \(\mathcal{A}_{\Box}[\mathcal{T}] \subset \mathcal{A}[\mathcal{T}]}\). Note that similar definitions of terminal assembly hold for other tile assembly models such as the 2HAM and derivatives of the 2HAM and aTAM.
