Self-assembling rulers for approximating generalized Sierpinski carpets

DOI10.1007/S00453-012-9691-XzbMath1275.68070OpenAlexW2771980504MaRDI QIDQ378210

Brad Shutters, Steven M. Kautz

Publication date: 11 November 2013

Published in: Algorithmica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00453-012-9691-x

zbMATH Keywords

Sierpinski carpetfractalsmolecular computingself-assembly

Mathematics Subject Classification ID

Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) (68Q10) Fractals (28A80) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (5)

Fractal dimension of assemblies in the abstract tile assembly model ⋮ Strict self-assembly of fractals using multiple hands ⋮ Self-assembly of 4-sided fractals in the two-handed tile assembly model ⋮ Scaled Tree Fractals Do not Strictly Self-assemble ⋮ Hierarchical growth is necessary and (sometimes) sufficient to self-assemble discrete self-similar fractals

Cites Work

• Unnamed Item
• Approximate self-assembly of the Sierpinski triangle
• Self-assembly of discrete self-similar fractals
• Strict self-assembly of discrete Sierpinski triangles
• Coding and geometrical shapes in nanostructures: a fractal DNA-assembly
• The Lucas property of a number array
• A route to fractal DNA-assembly
• The program-size complexity of self-assembled squares (extended abstract)
• Self-assembly of the Discrete Sierpinski Carpet and Related Fractals
• Running time and program size for self-assembled squares
• Complexity of Self‐Assembled Shapes

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