2026-07-27T05:06:44Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23077 2025-10-02T12:33:12Z ddc:004 open_access

Brief Announcement: Intrinsic Universality in Seeded Active Tile Self-Assembly Gomez, Tim Grizzell, Elise Haun, Asher Knobel, Ryan Peters, Tom Schweller, Robert Wylie, Tim Intrinsic Universality Tile Automata Cellular Automata Self-assembly The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal model of self-assembly. We present a single universal Tile Automata system containing approximately 4600 states that can simulate (a) the output assemblies created by any other Tile Automata system Γ, (b) the dynamics involved in building Γ’s assemblies, and (c) Γ’s internal state transitions. It does so in a non-committal way: it preserves the full non-deterministic dynamics of a tile’s potential attachment or transition by selecting its state in a single step, considering all possible outcomes until the moment of selection. The system uses supertiles, each encoding the complete system being simulated. The universal system builds supertiles from its seed, each representing a single tile in Γ, transferring the information to simulate Γ to each new tile. Supertiles may also asynchronously transition states according to the rules of Γ. This result also implies IU for pairwise asynchronous Cellular Automata. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tim Gomez and Elise Grizzell and Asher Haun and Ryan Knobel and Tom Peters and Robert Schweller and Tim Wylie 2025 Is Part Of LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SAND.2025.24 urn:nbn:de:0030-drops-230772 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.24 eng https://creativecommons.org/licenses/by/4.0/legalcode