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Directed Percolation And The Abstract Tile Assembly Model, Tyler Garrett Moore

Graduate Theses and Dissertations

Self-assembly is a process by which simple components build complex structures through local interactions. Directed percolation is a statistical physical model for describing competitive spreading processes on lattices. The author describes an algorithm which can transform a tile assembly system in the abstract Tile Assembly Model into a directed percolation problem, and then shows simulations of the aTAM which support this algorithm. The author also investigates two new constructs designed for Erik Winfree's abstract Tile Assembly Model called the NULL tile and temperature 1.5. These constructs aid the translation between self-assembly and directed percolation and may assist self-assembly researchers in …