2018/07/12 by Jacob Hendricks, Hendricks, Jacob, Joseph Opseth +6
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Cellular Automata and Applications #Computational Geometry (cs.CG) #DNA and Biological Computing #Emerging Technologies (cs.ET) #FOS: Computer and information sciences #Modular Robots and Swarm Intelligence #cs.CG #cs.ET
paper · pdf · doi:10.48550/arxiv.1807.04831
openalex publication_date 2018/07/12 · arxiv created 2018/07/17 · arxiv updated 2018/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove that in the abstract Tile Assembly Model (aTAM), an accretion-based model which only allows for a single tile to attach to a growing assembly at each step, there are no tile assembly systems capable of self-assembling the discrete self-similar fractals known as the "H" and "U" fractals. We then show that in a related model which allows for hierarchical self-assembly, the 2-Handed Assembly Model (2HAM), there does exist a tile assembly systems which self-assembles the "U" fractal and conjecture that the same holds for the "H" fractal. This is the first example of discrete self similar fractals which self-assemble in the 2HAM but not in the aTAM, providing a direct comparison of the models and greater understanding of the power of hierarchical assembly.