Approximate self-assembly of the Sierpinski triangle

DOI10.1007/978-3-642-13962-8_32zbMath1279.68082arXiv1001.2888OpenAlexW2049281111MaRDI QIDQ693068

Jack H. Lutz, Brad Shutters

Publication date: 7 December 2012

Published in: Theory of Computing Systems, Programs, Proofs, Processes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.2888

zbMATH Keywords

fractal dimensionSierpinski triangletile assembly

Mathematics Subject Classification ID

Fractals (28A80) Genetics and epigenetics (92D10) Hausdorff and packing measures (28A78)

Related Items (14)

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 ⋮ Self-assembling rulers for approximating generalized Sierpinski carpets ⋮ Scaled Tree Fractals Do not Strictly Self-assemble ⋮ Self-assembly of infinite structures: a survey ⋮ Improved lower and upper bounds on the tile complexity of uniquely self-assembling a thin rectangle non-cooperatively in 3D ⋮ Hierarchical self-assembly of fractals with signal-passing tiles ⋮ Optimal program-size complexity for self-assembled squares at temperature 1 in 3D ⋮ Hierarchical growth is necessary and (sometimes) sufficient to self-assemble discrete self-similar fractals ⋮ Self-assembly of and optimal encoding within thin rectangles at temperature-1 in 3D ⋮ Scaled pier fractals do not strictly self-assemble ⋮ Hierarchical Self-Assembly of Fractals with Signal-Passing Tiles ⋮ An introduction to tile-based self-assembly and a survey of recent results

Cites Work

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• Strict self-assembly of discrete Sierpinski triangles
• The equality of fractional dimensions for certain cellular automata
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• The program-size complexity of self-assembled squares (extended abstract)
• Self-assembly of the Discrete Sierpinski Carpet and Related Fractals
• Defining Fractal Subsets of Z ^d
• Self-Affine Carpets on the Square Lattice
• Distribution of digits in integers: fractal dimensions and zeta functions
• Complexity of Self‐Assembled Shapes
• Mathematical Foundations of Computer Science 2005

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