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Classification of cellular automata according to a computable index

Research Project

Project/Area Number 15K17591
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKyoto University of Education (2016-2017)
University of Shizuoka (2015)

Principal Investigator

Kawaharada Akane  京都教育大学, 教育学部, 講師 (70710953)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsセル・オートマトン / 特異関数 / フラクタル図形 / 力学系 / 数理モデル / 有限領域 / 空間一様性
Outline of Final Research Achievements

In this research, we gave a classification of two-dimensional symmetrical elementary cellular automata (ECAs), and studied the spatio-temporal patterns. The spatio-temporal patterns from the single site seeds eventually fall under four cases. We shown that in the 1024 spatio-temporal patterns, there exist less than 346 different fractal-like patterns. Numerical simulations shown that essential fractal-like patterns created by the ECAs are related to a singular function.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (17 results)

All 2017 2016 2015

All Journal Article (4 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 4 results,  Acknowledgement Compliant: 3 results) Presentation (13 results) (of which Int'l Joint Research: 6 results,  Invited: 2 results)

  • [Journal Article] Fractal Structure of a Class of Two-Dimensional Two-State Cellular Automata2017

    • Author(s)
      Kawaharada Akane、Namiki Takao
    • Journal Title

      2017 Fifth International Symposium on Computing and Networking

      Volume: 1 Pages: 205-208

    • DOI

      10.1109/candar.2017.89

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analysis of a method for constructing a cellular automaton from a continuous system2016

    • Author(s)
      Akane Kawaharada, Tomoyuki Miyaji, Naoto Nakano
    • Journal Title

      International Journal of Networking and Computing

      Volume: Volume 6, Number 2

    • NAID

      130005475334

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] An analyzable method for constructing a cellular automaton from a continuous system2015

    • Author(s)
      Akane Kawaharada, Tomoyuki Miyaji, and Naoto Nakano
    • Journal Title

      2015 Third International Symposium on Computing and Networking

      Volume: 1 Pages: 418-423

    • DOI

      10.1109/candar.2015.111

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Proper choice of spatio-temporal scale and dataset subsampling for empirical CA construction2015

    • Author(s)
      Akane Kawaharada, Tomoyuki Miyaji, and Naoto Nakano
    • Journal Title

      2015 Third International Symposium on Computing and Networking

      Volume: 1 Pages: 424-429

    • DOI

      10.1109/candar.2015.113

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Mathematical characterization of space-time patterns created by multi-dimensional nonlinear cellular automata2017

    • Author(s)
      Akane Kawaharada
    • Organizer
      Women in Mathematics - a Panorama of Contributions
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] セル・オートマトンで生成される自己相似図形について2017

    • Author(s)
      川原田 茜
    • Organizer
      研究集会「数学と現象 in X (Mathematics and Phenomena in X,略称:MPX)」
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Fractal structure of a class of 2D 2-state cellular automata2017

    • Author(s)
      Akane Kawaharada and Takao Namiki
    • Organizer
      The Fifth International Symposium on Computing and Networking
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] セル・オートマトンの生成図形と特異関数との関係について2016

    • Author(s)
      川原田 茜
    • Organizer
      2015年度冬の力学系研究集会
    • Place of Presentation
      日本大学軽井沢研修所
    • Year and Date
      2016-01-08
    • Related Report
      2015 Research-status Report
  • [Presentation] 実データに基づくセル・オートマトンモデルの構成とその応用2016

    • Author(s)
      川原田 茜
    • Organizer
      第1回京都教育大学数学談話会
    • Place of Presentation
      京都教育大学
    • Related Report
      2016 Research-status Report
  • [Presentation] 偏微分方程式を模倣するセル・オートマトンモデルの構成と解析2016

    • Author(s)
      川原田 茜
    • Organizer
      第29回京都大学応用数学セミナーと京都力学系セミナーの合同セミナー
    • Place of Presentation
      京都大学
    • Related Report
      2016 Research-status Report
  • [Presentation] 二次元セル・オートマトンが生成する図形のフラクタル性について2015

    • Author(s)
      川原田 茜
    • Organizer
      2015年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学
    • Year and Date
      2015-12-17
    • Related Report
      2015 Research-status Report
  • [Presentation] An analyzable method for constructing a cellular automaton from a continuous system2015

    • Author(s)
      Akane Kawaharada, Tomoyuki Miyaji, and Naoto Nakano
    • Organizer
      2015 Third International Symposium on Computing and Networking
    • Place of Presentation
      Sapporo Business Innovation Center
    • Year and Date
      2015-12-09
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Proper choice of spatio-temporal scale and dataset subsampling for empirical CA construction2015

    • Author(s)
      Akane Kawaharada, Tomoyuki Miyaji, and Naoto Nakano
    • Organizer
      2015 Third International Symposium on Computing and Networking
    • Place of Presentation
      Sapporo Business Innovation Center
    • Year and Date
      2015-12-09
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 解析可能なセル・オートマトン構成法による偏微分方程式の模倣2015

    • Author(s)
      川原田 茜, 宮路 智行, 中野 直人
    • Organizer
      可積分系が拓く現象数理モデル
    • Place of Presentation
      明治大学
    • Year and Date
      2015-11-05
    • Related Report
      2015 Research-status Report
  • [Presentation] An empirical construction of a cellular automaton from a continuous system and its mathematical analysis2015

    • Author(s)
      Akane Kawaharada, Tomoyuki Miyaji, and Naoto Nakano
    • Organizer
      International Conference on Mathematical Modeling and Applications 2015 `Self-Organization-Modeling and Analysis'
    • Place of Presentation
      Meiji University
    • Year and Date
      2015-10-26
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 二次元セル・オートマトンが生成する図形のフラクタル性について2015

    • Author(s)
      川原田 茜
    • Organizer
      日本数学会 2015年度 秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] Statistical method for constructing cellular automata2015

    • Author(s)
      Akane Kawaharada
    • Organizer
      The 8th International Congress On Industrial And Applied Mathematics
    • Place of Presentation
      the China National Convention Center
    • Year and Date
      2015-08-10
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research

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Published: 2015-04-16   Modified: 2019-03-29  

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