Concentration programming

aTAM progresses under the assumption that all reactants (tiles, assemblies, etc.) coexist in a test tube environment at equal and constant concentrations. Significant power may be added to the model if we allow variation in the form of tile concentration. Under normal conditions in the aTAM, assemblies only progress and grow via local interactions between glues on different tiles. Differing the global concentration of tiles in the test solution introduces another globally accessible information source.

Model Overview

Introduced in , Tile Concentration Programming allows variable tile concentrations and thus the inclusion of additional information as input to a tile assembly system as the relative concentrations of the various tile types. These concentrations can be "sampled" by a static construction in a variant of aTAM which allows for a competitive binding race at specific locations on the construction. Multiple tile types may bind to these sampling slots, the final distribution of which serves as the assembly's "sample" of the environmental concentration distribution.

Results

Doty, in , showed the significant increase in power granted to aTAM systems by Concentration Programming. He showed that it is possible to construct (with arbitrarily high probability) nxn squares with a constant tile set, as well as scaled shapes where the concentration program and tile set depend on the shapes. The ability to vary concentration has also been demonstrated to decrease assembly time and the chance for errors , by Chen and Kao. Other results have shown the capability of this model to produce approximate and exact shapes with greatly reduced tile complexity and assembly time.

An example of a concentration sampling gadget, presented in . With S as the seed tile, these tiles form the sampling line. The concentrations of each tile are noted as CA, CA′, and CB. These tiles create a line, sampling a red tile with a density of 1/n. A binary counter sums up the total length, as well as the total number of red tiles. These two values are then divided to yield an estimation.