Difference between revisions of "Tile Assembly System (TAS)"
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==Overview== | ==Overview== | ||
| − | Informally, a tile assembly system can be thought of as an instance of a [[Tile Assembly Models | tile assembly model]]. Unless otherwise denoted, a tile assembly system refers to a tile assembly system of the [[Abstract Tile Assembly Model | abstract tile assembly model]]. | + | Informally, a tile assembly system can be thought of as an instance of a [[:Category:Tile Assembly Models | tile assembly model]]. Unless otherwise denoted, a tile assembly system refers to a tile assembly system of the [[Abstract Tile Assembly Model | abstract tile assembly model]]. |
==Abstract Tile Assembly Model Tile Assembly System (aTAM TAS)== | ==Abstract Tile Assembly Model Tile Assembly System (aTAM TAS)== | ||
| − | A tile assembly system (TAS) of the [[Abstract Tile Assembly Model | abstract tile assembly model]] is an ordered triple $\mathcal{T} = (T, \sigma, \tau)$, where $T$ is a finite set of tile types, $\sigma$ is a seed assembly with finite domain, and $\tau \in \N$. | + | A tile assembly system (TAS) of the [[Abstract Tile Assembly Model | abstract tile assembly model]] is an ordered triple $\mathcal{T} = (T, \sigma, \tau)$, where $T$ is a finite set of tile types, $\sigma$ is a seed assembly with finite domain, and $\tau \in \mathbb{N}$. |
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| + | ==Abstract Tile Assembly Model Generalized Tile Assembly System (aTAM GTAS)== | ||
| + | A generalized tile assembly system (GTAS) of the [[Abstract Tile Assembly Model | abstract tile assembly model]] is an ordered triple $\mathcal{T} = (T, \sigma, \tau)$, where $T$ is a not necessarily finite set of tile types, $\sigma$ is a seed assembly with finite domain, and $\tau \in \mathbb{N}$. Note the only difference between the aTAM GTAS and the aTAM TAS is that the aTAM TAS requires the tile set to be finite. | ||
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| + | [[Category: Terminology]] | ||
| + | [[Category:Self-assembly]] | ||
Latest revision as of 14:21, 27 May 2014
Contents
Overview
Informally, a tile assembly system can be thought of as an instance of a tile assembly model. Unless otherwise denoted, a tile assembly system refers to a tile assembly system of the abstract tile assembly model.
Abstract Tile Assembly Model Tile Assembly System (aTAM TAS)
A tile assembly system (TAS) of the abstract tile assembly model is an ordered triple \(\mathcal{T} = (T, \sigma, \tau)\), where \(T\) is a finite set of tile types, \(\sigma\) is a seed assembly with finite domain, and \(\tau \in \mathbb{N}\).
Abstract Tile Assembly Model Generalized Tile Assembly System (aTAM GTAS)
A generalized tile assembly system (GTAS) of the abstract tile assembly model is an ordered triple \(\mathcal{T} = (T, \sigma, \tau)\), where \(T\) is a not necessarily finite set of tile types, \(\sigma\) is a seed assembly with finite domain, and \(\tau \in \mathbb{N}\). Note the only difference between the aTAM GTAS and the aTAM TAS is that the aTAM TAS requires the tile set to be finite.
