Pattern Formation by Spatially Organized Approximate Majority Reactions

Pattern formation is a topic of great interest in biology and nanotechnology. In this paper we investigate a system of spatially-organized reactions inspired by a well-known distributed algorithm for approximate majority voting, and demonstrate that this system can lead to pattern formation from a randomly initialized starting state. We also show that the approximate majority reaction scheme can preserve an existing pattern in the face of noise, and that exerting control over reaction rates can influence the generated pattern. This work has potential applications in the rational design of pattern-forming systems in DNA nanotechnology and synthetic biology.

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