Analysis of Effect of Symmetric Tiles on Binary Counter in DNA Self-Assembly

Abstract

With the growth of complicate system or crystals, whereas, a few phenomena have occurred and been found, which could result in final crystals or patterns with errors. Among those phenomena, one has still not been processed in current published literatures, which is named symmetry tile may appear. This paper analyses the effect of symmetry tile on binary counter in DNA Self-Assembly. The exact relationship between symmetry tile and counting is set up considering the type of symmetry and the position of the symmetry tile. The analysis shows that the final patterns are partly or completely different from the originally desired patterns in the case of symmetry tile due to the changed counting behavior. Simulation results which are obtained by Xgrow demonstrate that the analysis is valid and correct.