Date of Award
Master of Science (MS)
Dr. Robert Schweller
Dr. Bin Fu
Dr. Andrew Winslow
The problem of the strict self-assembly of infinite fractals within tile self-assembly is considered. In particular, tile assembly algorithms are provided for the assembly of the discrete Sierpinski triangle and the discrete Sierpinski carpet.
The robust random number generation problem in the abstract tile assembly model is introduced. First, it is shown this is possible for a robust fair coin flip within the aTAM, and that such systems guarantee a worst case O(1) space usage. This primary construction is accompanied with variants that show trade-offs in space complexity, initial seed size, temperature, tile complexity, bias, and extensibility.
This work analyzes the number of tile types t, bins b, and stages necessary and sufficient to assemble n × n squares and scaled shapes in the staged tile assembly model.
Further, this work shows how to design a universal shape replicator in a 2-HAM self-assembly system with both attractive and repulsive forces.
Chalk, Cameron, "Fractals, Randomization, Optimal Constructions, and Replication in Algorithmic Self-Assembly" (2017). Theses and Dissertations - UTRGV. 214.