Optimum coding framework for error detection in the self-assembly of the Sierpinski triangle

This study presents a coding framework by which DNA self-assembly can be analysed for error detection. The proposed framework relies on coding and mapping functions that allow establishing the correctness of bonding each tile based on the codes of the tiles along a so-called traversal path. This method is different from the one that relies on comparing the pattern to be assembled (as defined by the tile set) and the current aggregate (as resulting from previously assembled tiles). As a widely used pattern and instantiation of this process, the Sierpinski triangle self-assembly is analysed in detail. The Sierpinski triangle is therefore utilised as an example to show the application of the proposed method. Different properties are proposed and its optimum coding is achieved for error detection. Simulation results are presented.