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Traversal Languages Capturing Isomorphism Classes of Sierpiński Gaskets

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Unconventional Computation and Natural Computation (UCNC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9726))

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Abstract

We consider recursive structural assembly using regular d-dimensional simplexes such that a structure at every level is obtained by joining \(d + 1\) structures from a previous level. The resulting structures are similar to the Sierpiński gasket. We use intersection graphs and index sequences to describe these structures. We observe that for each \(d>1\) there are uncountably many isomorphism classes of these structures. Traversal languages that consist of labels of walks that start at a given vertex can be associated with these structures, and we find that these traversal languages capture the isomorphism classes of the structures.

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Acknowledgement

We would like to thank Chaim Goodman-Strauss and Lorenzo Sadun for their kind assistance. This work has been supported in part by the NSF grants CCF-1526485 and the NIH grant GM109459.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA

    Nataša Jonoska, Milé Krajčevski & Gregory McColm

Authors
  1. Nataša Jonoska
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  2. Milé Krajčevski
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  3. Gregory McColm
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Corresponding author

Correspondence to Gregory McColm .

Editor information

Editors and Affiliations

  1. Manchester Metropolitan University, Manchester, United Kingdom

    Martyn Amos

  2. University of British Columbia, Vancouver, BC, Canada

    ANNE CONDON

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Jonoska, N., Krajčevski, M., McColm, G. (2016). Traversal Languages Capturing Isomorphism Classes of Sierpiński Gaskets. In: Amos, M., CONDON, A. (eds) Unconventional Computation and Natural Computation. UCNC 2016. Lecture Notes in Computer Science(), vol 9726. Springer, Cham. https://doi.org/10.1007/978-3-319-41312-9_13

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  • DOI: https://doi.org/10.1007/978-3-319-41312-9_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41311-2

  • Online ISBN: 978-3-319-41312-9

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