Skip to main content
SpringerLink
Log in
Book cover

Katachi ∪ Symmetry pp 333–340Cite as

An Application of Penrose Tiling to Artistic Design — One Standing and Four Sprawling Dogs —

  • Conference paper

  • 189 Accesses

Abstract

A new quasi-periodic design based on the illustration of dogs is presented. We present an artistic quasi-periodic tiling of which the frame of the illustration is based on a quasiperiodic lattice (QPL1) with decagonal symmetry. The elements of the illustration are composed of one standing dog and four sprawling ones which correspond to one thin rhombus and four thick rhombi of the decagonal QPL1 respectively. The algorithm for building quasi-periodic tiling of the dogs is characterized by the matching rule in the self-similar inflation method. For this illustration we show that three kinds of arrows are necessary in order that every piece of tile looks like a dog.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Penrose, R. (1974).’ The Role of Aesthetics in Pure and Applied Mathematical Research’ Bull Inst. Math. Appl 10, 266–271

    Google Scholar 

  2. Gardner, M. (1977)’ Extraordinary nonperiodic tiling that enriches the theory of tiles’ Sci. Amer. 236, 110–121

    Article  Google Scholar 

  3. Bruijn, N.G. de. (1981)’ Algebraic theory of Penrose’s non-periodic tiling of the plane. I’, Proc. K. Ned. Akad. Wet. Ser. A84, 39–52, 53-66

    Google Scholar 

  4. Shechtman, D., Blech, I., Gratias, D. and Chan, J.W. (1984)’ Metallic Phase with Long-Range Order and No Translational Symmetry’. Phys. Rev. Lett. 53, 1951–1953

    Article  Google Scholar 

  5. Zobetz, E. (1992)’ A Pentagonal Quasi-periodic Tiling with Fractal Acceptance Domain’ Acta Cryst. A48, 328–335

    Article  Google Scholar 

  6. Watanabe, Y. and Ikegami, Y. (1991)’ Matching Rule for a Self-similar 3D Pseudo-Octagonal Quasilattice’, in Proceedings of China-Japan Seminars “QUASICRYSTALS”, World Scientific Singapore, 204–211

    Google Scholar 

  7. Zobetz, E. (1990)’ Vertex Frequencies in Generalized Penrose Patterns’ Acta Cryst.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute of Physical and Chemical Research Wako-shi, Saitama 351-01, Japan

    Yasunari Watanabe, Yuji Ikegami & Kiyoji Takahashi

Authors
  1. Yasunari Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuji Ikegami
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kiyoji Takahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Applied Physics, University of Tsukuba, 1-1-1 Ten-nodai, Tsukuba, Ibaraki 305, Japan

    Tohru Ogawa (Professor) (Professor)

  2. Institute of Space and Astronautical Science Structural Morphology Research, University of Tokyo and Professor Emeritus, 3-9-7 Tsurukawa, Machida, Tokyo 195, Japan

    Koryo Miura (Professor Emeritus) (Professor Emeritus)

  3. Institute of Modern Languages and Cultures, University of Tsukuba, 1-1-1 Ten-nodai, Tsukuba, Ibaraki 305, Japan

    Takashi Masunari (Professor) (Professor)

  4. Institute of Applied Physics, University of Tsukuba, 1-1-1 Ten-nodai, Tsukuba, Ibaraki 305, Japan

    Dénes Nagy (Professor, Director) (Professor, Director)

  5. Symmetrion-The Institute for Advanced Symmetry Studies, P.O. Box 4, Budapest, H-1361, Hungary

    Dénes Nagy (Professor, Director) (Professor, Director)

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Tokyo

About this paper

Cite this paper

Watanabe, Y., Ikegami, Y., Takahashi, K. (1996). An Application of Penrose Tiling to Artistic Design — One Standing and Four Sprawling Dogs —. In: Ogawa, T., Miura, K., Masunari, T., Nagy, D. (eds) Katachi ∪ Symmetry. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68407-7_39

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-68407-7_39

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68409-1

  • Online ISBN: 978-4-431-68407-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation