View source for Dupled abstract Tile Assembly Model (DaTAM)

Dupled abstract Tile Assembly Model (DaTAM) is a slight extension to the abstract Tile Assembly Model (aTAM) that allows for not only the standard square tiles, but also “duple” tiles which are rectangles pre-formed by the joining of two square tiles. The addition of duples allows for powerful behaviors of self-assembling systems at temperature 1, meaning systems which exclude the requirement of cooperative binding by tiles (i.e., the requirement that a tile must be able to bind to at least 2 tiles in an existing assembly if it is to attach). The rectangular tiles are $2 \times 1$ or $1 \times 2$ rectangles which can logically be thought of as two square tiles which begin pre-attached to each other along an edge, hence
the name duples. A dupled tile assembly system (DTAS) is an ordered 5-tuple $(T, S, D, \sigma, \tau )$ where $T$, $\sigma$, and $\tau$ are as for a TAS, and S is the set of singleton
(i.e. square) tiles which are available for assembly, and $D$ is the set of duple tiles. The tile types which make up $S$ and $D$ all belong to $T$, with those in $D$ each being a combination of two tile types from $T$.

A dupled tile assembly system (DTAS) is a tuple $T = (T, S, D, \sigma, \tau )$, where $T$ is a finite tile set, $S \subseteq T$ is a finite set of singleton types, $D$ is a finite set of duple tile types, $\sigma: \mathcal{Z}^2 \longrightarrow T$is the finite, $\tau$-stable, seed assembly, and $\tau \in \mathcal{Z}^{+}$ is the temperature.