Difference between revisions of "Synchronous Tile Assembly Model (syncTAM)"
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| alt2 = Shape producible only in the syncTAM | | alt2 = Shape producible only in the syncTAM | ||
| caption2 = An example of a shape that can self-assemble in the syncTAM but not aTAM (without also making other shapes) | | caption2 = An example of a shape that can self-assemble in the syncTAM but not aTAM (without also making other shapes) | ||
| − | | image3 = | + | | image3 = SyncTAM_imposs_shape.png |
| − | | alt3 = | + | | alt3 = No syncTAM can match this aTAM system |
| − | | caption3 = | + | | caption3 = Schematic depiction of an aTAM system capable of making an infinite set of shapes, many of which would be impossible in any syncTAM system |
}} | }} | ||
Revision as of 03:10, 19 April 2025
The aTAM is meant to be a simplified mathematical model of tile-based self-assembly, and therefore it uses many simplifying assumptions. One of these is that the assembly process is broken into discrete steps, during each of which a single tile attaches to a growing assembly. Although if time is assumed to be continuous it is unlikely that two tiles would attach to an assembly at exactly the same time, as an assembly becomes larger and larger, more and more nearly simultaneous tile attachments will occur. This frequency would also increase in physically implemented systems if the concentrations of the free tiles was increased. In order to examine the end of the spectrum opposite to the aTAM in which a single tile is allowed to attach in each time step, the synchronous Tile Assembly Model, in which arbitrary numbers of tiles may attach during a single step, was introduced.
Contents
Model Definition
In the aTAM, the set of locations adjacent to the perimeter of an assembly into which tiles can validly bind is called the growth frontier, or simply frontier, of the assembly. While the aTAM requires that at each step of assembly a single frontier location is selected at random to receive a tile, in the synchronous Tile Assembly Model (syncTAM), it is required that at each step of assembly every frontier location receives a tile. As the frontier of a system can grow arbitrarily large, the number of tiles added per assembly step may also grow arbitrarily large. As in the aTAM, if any single frontier location allows for \(\tau\)-strength binding of tiles of multiple types, one of those types is non-deterministically chosen for each such location.
Survey of Results
The ability of the kTAM to accurately model the errors seen in laboratory settings coupled with its clean theoretical definition make it an ideal model in which to study mechanisms of error prevention and correction. Additionally, the algorithmic nature of self-assembly in the kTAM provides the opportunity to effectively apply a variety of algorithms from seemingly unrelated fields such as data transmission to make kTAM systems more robust.
