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Fractals in Seeded Tile Automata

Authors Asher Haun , Ryan Knobel, Adrian Salinas, Ramiro Santos, Robert Schweller, Tim Wylie

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ACM Subject Classification
  • Theory of computation
Keywords
  • self-assembly
  • tile automata
  • fractals

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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 all discrete self-similar fractals (DSSFs) with feasible generators are strictly buildable at scale 1 and temperature 1 in seeded TA. We then show that these results imply the existence of a single seeded TA system Γ that can strictly build any DSSF infinitely at scale 1 and temperature 1.

Cite As Get BibTex

Asher Haun, Ryan Knobel, Adrian Salinas, Ramiro Santos, Robert Schweller, and Tim Wylie. Fractals in Seeded Tile Automata. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.14

Author Details

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

Funding

This research was supported in part by National Science Foundation Grant CCF-2329918.

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