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.
@InProceedings{haun_et_al:LIPIcs.SAND.2025.14, author = {Haun, Asher and Knobel, Ryan and Salinas, Adrian and Santos, Ramiro and Schweller, Robert and Wylie, Tim}, title = {{Fractals in Seeded Tile Automata}}, booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)}, pages = {14:1--14:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-368-3}, ISSN = {1868-8969}, year = {2025}, volume = {330}, editor = {Meeks, Kitty and Scheideler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.14}, URN = {urn:nbn:de:0030-drops-230677}, doi = {10.4230/LIPIcs.SAND.2025.14}, annote = {Keywords: self-assembly, tile automata, fractals} }
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