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A study on cellular automata on quasi-periodic tilings

Research Project

Project/Area Number 26330016
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Theory of informatics
Research InstitutionHiroshima University

Principal Investigator

Imai Katsunobu  広島大学, 工学研究院, 助教 (20253106)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsセルオートマトン / 準周期タイリング / 等方性 / 準周期タイル / コロナ
Outline of Final Research Achievements

We studied cellular automata working on quasi-periodic tilings. We are interested in the difference/similarity of signal propagation of cellular automata working on between the normal periodic cells and quasi-periodic tilings. We introduce corona limit which naturally visualizes the growth pattern of signal propagation. We show that the corona limit of a Penrose tilings is a regular decagon. We also show that a condition of the existence of corona limits and their shapes are point symmetric convex polygons when they are periodic. We compute the corona and edge corona limits of all the 1- and 2-regular tilings. There exists corona limits whose number of vertices are 4, 6, 8, 10, 12 and 16.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report

Research Products

(15 results)

All 2017 2016 2015 2014

All Presentation (12 results) (of which Int'l Joint Research: 6 results) Book (1 results) Funded Workshop (2 results)

  • [Presentation] On weak universality of three-dimensional Larger than Life cellular automaton2017

    • Author(s)
      K. Imai, K. Oroji and T. Kubota
    • Organizer
      23rd annual international workshop on cellular automata and discrete complex systems AUTOMATA 2017
    • Place of Presentation
      University of Milano-Bicocca, Milano, Italy
    • Year and Date
      2017-06-07
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Corona Limit and Crystal Growth2017

    • Author(s)
      K. Imai
    • Organizer
      11th International Workshop on Natural Computing (IWNC11)
    • Place of Presentation
      Akita International University, Akita, Japan
    • Year and Date
      2017-05-13
    • Related Report
      2016 Annual Research Report
  • [Presentation] Particle Complexity of Universal Finite Number-Conserving Cellular Automata2016

    • Author(s)
      A. Alhazov, K Imai
    • Organizer
      4th International Workshop on Applications and Fundamentals of Cellular Automata AFCA '16
    • Place of Presentation
      Higashi Hiroshima Arts and Culture Hall, Hiroshima, Japan
    • Year and Date
      2016-11-22
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Corona limits of tilings: Periodic case2016

    • Author(s)
      S. Akiyama, K. Imai
    • Organizer
      Mathematical Physics of Quasi-Periodic Systems and Related Topics
    • Place of Presentation
      RIMS, Kyoto University, Japan
    • Year and Date
      2016-11-07
    • Related Report
      2016 Annual Research Report
  • [Presentation] The Corona Limit of Penrose Tilings Is a Regular Decagon2016

    • Author(s)
      S. Akiyama, K. Imai
    • Organizer
      22nd International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2016
    • Place of Presentation
      University of Zurich, Switzerland
    • Year and Date
      2016-06-15
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The corona limit of Penrose tilings is a regular decagon2016

    • Author(s)
      Shigeki Akiyama and Katsunobu Imai
    • Organizer
      The 22nd annual international workshop on cellular automata and discrete complex systems, AUTOMATA 2016
    • Place of Presentation
      University of Zurich
    • Year and Date
      2016-06-15
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On Enumeration of Motion Representable Two-Dimensional Two-State Number-Conserving Cellular Automata2015

    • Author(s)
      Hisamichi Ishizaka, Yohei Takemura, Katsunobu Imai
    • Organizer
      3rd International Workshop on Application and Fundamentals of Cellular Automata
    • Place of Presentation
      Sapporo Business Innovation Center, Japan
    • Year and Date
      2015-12-08
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] An Approach to Constructing and Simulating Block Cellular Automata by Gellular Automata2015

    • Author(s)
      Shaoyu Wang, Katsunobu Imai, Masami Hagiya
    • Organizer
      3rd International Workshop on Application and Fundamentals of Cellular Automata
    • Place of Presentation
      Sapporo Business Innovation Center, Japan
    • Year and Date
      2015-12-08
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] The shape of n-th corona of any patch on Penrose tilings converges to the regular decagon2015

    • Author(s)
      Katsunobu Imai
    • Organizer
      Aperiodic tile sets and related topics
    • Place of Presentation
      RIMS, Kyoto University, Japan
    • Year and Date
      2015-10-19
    • Related Report
      2015 Research-status Report
  • [Presentation] On the composition of signals in gellular automata2014

    • Author(s)
      Shaoyu Wang, Katsunobu Imai and Masami Hagiya
    • Organizer
      2nd International Workshop on Applications and Fundamentals of Cellular Automata
    • Place of Presentation
      Grandship, Shizuoka Convention & Arts Center, Shizuoka, Japan
    • Year and Date
      2014-12-10 – 2014-12-12
    • Related Report
      2014 Research-status Report
  • [Presentation] On the homogeneous propagation of signals in cellular automata on quasi periodic tilings2014

    • Author(s)
      Katsunobu Imai
    • Organizer
      Mathematical Model of quasi-crystals and related topics
    • Place of Presentation
      RIMS, Kyoto University, Japan
    • Year and Date
      2014-10-27 – 2014-10-29
    • Related Report
      2014 Research-status Report
  • [Presentation] On DNA-based Gellular Automata2014

    • Author(s)
      Masami Hagiya, Shaoyu Wang, Ibuki Kawamata, Satoshi Murata, Teijiro Isokawa, Ferdinand Peper and Katsunobu Imai
    • Organizer
      Unconventional Computation & Natural Computation
    • Place of Presentation
      University of Western Ontario, London, Ontario, Canada
    • Year and Date
      2014-07-14 – 2014-07-18
    • Related Report
      2014 Research-status Report
  • [Book] Designing Beauty: The Art of Cellular Automata2016

    • Author(s)
      Adamatzky, Andrew, Martinez, Genaro J. (Eds.)
    • Total Pages
      191
    • Publisher
      Springer International Publishing
    • Related Report
      2015 Research-status Report
  • [Funded Workshop] Mini Workshop on Symbolic Dynamics and Related Topics2015

    • Place of Presentation
      Faculty of Engineering, Hiroshima University
    • Year and Date
      2015-10-23
    • Related Report
      2015 Research-status Report
  • [Funded Workshop] Aperiodic tile sets and related topics2015

    • Place of Presentation
      RIMS, Kyoto University
    • Year and Date
      2015-10-19
    • Related Report
      2015 Research-status Report

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Published: 2014-04-04   Modified: 2018-03-22  

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