Fractals, Reachability, and Computation in Models of DNA Self-Assembly and Chemical Reaction Networks

Author

Ryan Arlie Knobel, The University of Texas Rio Grande Valley

Date of Award

12-1-2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Computer Science

First Advisor

Tim Wylie

Second Advisor

Robert Schweller

Third Advisor

Bin Fu

Abstract

This thesis serves as the bridge between results compiled across varying models of tile self-assembly, molecular computation, and game complexity. As such, this thesis is broken into three chapters. In the first part, we show how to generate any Discrete Self-Similar Fractal (DSSF) with a feasible generator in the seeded Tile Assembly model, a model limited to single tile attachments and pairwise state transitions. In the next part, we study models of molecular computation, where we consider the problem of reachability in Chemical Reaction Networks and similar model extensions. The final part is a game-complexity analysis of Celtic! and k-ago, two games which have interesting connections to tile self-assembly, knot theory, and generalized k-in-a-row.

Comments

Copyright 2025 Ryan A. Knobel. All Rights Reserved. https://proquest.com/docview/3292466491

Recommended Citation

Knobel, R. A. (2025). Fractals, Reachability, and Computation in Models of DNA Self-Assembly and Chemical Reaction Networks [Master's thesis, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/1827