Fractals in seeded tile automata

Authors

• Asher Haun, The University of Texas Rio Grande Valley
• Ryan Knobel, The University of Texas Rio Grande Valley
• Adrian Salinas, The University of Texas Rio Grande Valley
• Ramiro Santos, The University of Texas Rio Grande Valley
• Robert Schweller, The University of Texas Rio Grande ValleyFollow
• Tim Wylie, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

8-6-2026

Abstract

This work fully characterizes fractal generation in the seeded Tile Automata model (seeded TA), a model similar to the abstract Tile Assembly model (aTAM) with the added ability for adjacent tiles to change states. Under these assumptions, we first show that for every discrete self-similar fractal (DSSF) with a feasible generator, there exists a seeded TA system with temperature-1 that strictly builds it. We then show that these results imply the existence of a seeded TA system Γ that can strictly build any DSSF infinitely at scale-1 and temperature-1.

Comments

© 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Recommended Citation

Haun, Asher, Ryan Knobel, Adrian Salinas, Ramiro Santos, Robert Schweller, and Tim Wylie. "Fractals in Seeded Tile Automata." Theoretical Computer Science (2026): 116042. https://doi.org/10.1016/j.tcs.2026.116042

Publication Title

Theoretical Computer Science

DOI

https://doi.org/10.1016/j.tcs.2026.116042