Blocked Tile Assembly Model (BlockTAM)

In tile-based models of self-assembly such as the aTAM, all input to a system is provided at the beginning of the process in the form of pre-made seed assemblies and copies of unbound tiles of a fixed set of tile types, and then self-assembly proceeds during the duration of a relatively constant temperature. The Blocked Tile Assembly Model, or BlockTAM, is a mathematical model of tile-based self-assembling systems that allows for additional dynamics and types of input to its systems. The major differences from the aTAM are that a series of temperatures can be specified so that the assembly process proceeds through each of them in sequence, and that so-called blockers, which are components that disable glues when the temperatures are in fixed ranges, can be included with systems. These changes allow for a notable increase in the possible dynamics for BlackTAM systems.

Model Definition

The definition of the Block Tile Assembly Model (BlockTAM) is similar to the multiple temperature model...

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Example BlockTAM system

The following figure shows an example of a BlockTAM system.

An example BlockTAM system.

TBD: Add a description.

Survey of Results

Initial results in the BlockTAM have shown how so-called universal tile sets can be designed for certain tasks, such as encoding numbers or making assemblies of given shapes, so that the only input specified to them is provided via a series of temperature changes. Those temperature changes are used to drive the self-assembly processes of BlockTAM systems to achieve the specified tasks. Following is a brief overview of some of these results.

Universal number encoding

TBD: give an overview of this construction...

A bit-reading gadget in the temperature-1 syncTAM.

Universal shape building

TBD: give an overview of this construction...

An example shape that requires the synchronization of the syncTAM to self-assemble. Any system trying to self-assemble such a shape in the aTAM would also have to produce many non-target shapes.

Examples and Simulation Software

The BlockTAM can be simulated by (the currently beta version of) | WebTAS.

Examples of systems cited above, as well as scripts for generating universal number encoders, universal shape builders, and the temperature sequences used to control them can be downloaded from | BlockTAM_examples. (Clicking on the most recent, bottommost link will download a zip file containing the files.)