Top

Published in:

2018 | OriginalPaper | Chapter

Fractal Arrangement for 2D Cellular Automata and Its Implementation for Outer-Totalistic Rules

Authors : Yoshihiko Kayama, Yuka Koda, Ikumi Yazawa

Published in: Cellular Automata

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Cellular automata (CAs) have played a significant role in studies of complex systems. Recently, a recursive estimation of neighbors algorithm that distinguishes the perception area of each cell from the CA rule neighborhood was introduced to extend CA. This framework makes it possible to construct non-uniform CA models composed of cells with different sizes of the perception area, which can be interpreted as an individual attribute of each cell. For example, focusing primarily on one-dimensional (1D) elementary CA, fractal CAs composed of self-similarly arranged cells have been proposed and their characteristics have been investigated. In this paper, 2D fractal CAs are defined and implemented for outer-totalistic CA rules. Fractal CAs derived from a linear rule inherit that rule’s features, including replicability and time reversibility, which indicate their applicability to various fields.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Quantum Walks on Quantum Cellular Automata Lattices: Towards a New Model for Quantum Computation

next chapter Self-verifying Cellular Automata

CAs with the von Neumann neighborhood (Fig. 1b) can be extended through similar steps.

The time reversibility of F-CA[B1357S02468] was proved until level 2 by a round-robin check of all configurations.

von Neumann, J.: The theory of self-reproducing automata. In: Burks, A.W. (ed.) Essays on Cellular Automata. University of Illinois Press (1966)

Kayama, Y.: Extension of cellular automata by introducing an algorithm of recursive estimation of neighbors. In: Proceedings of the 21st International Symposium on Artificial Life and Robotics, pp. 73–77 (2016)

Kayama, Y.: Expansion of perception area in cellular automata using recursive algorithm. In: Proceedings of the Fifteenth International Conference on the Simulation and Synthesis of Living Systems, pp. 92–99 (2016)

Reynolds, C.W.: Flocks, herds and schools: a distributed behavioral model. ACM SIGGRAPH Comput. Graph. 21(4), 25–34 (1987)CrossRef

Kayama, Y.: Cellular automata in fractal arrangement. In: Proceedings of the 23rd International Symposium on Artificial Life and Robotics (2018)

Gardner, M.: Mathematical games. Sci. Am. 223, 102–123 (1970)CrossRef

Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays. Academic, New York (1982)MATH

Adamatzky, A. (ed.): Game of Life Cellular Automata. Springer, London (2010). https://doi.org/10.1007/978-1-84996-217-9CrossRefMATH

Eppstein, D.: Growth and decay in life-like cellular automata. In: Adamatzky, A. (ed.) Game of Life Cellular Automata, pp. 71–98. Springer, London (2010). https://doi.org/10.1007/978-1-84996-217-9_6CrossRef

10.

Mandelbrot, B.B., Pignoni, R.: The Fractal Geometry of Nature, vol. 173. WH Freeman, New York (1983)

11.

Fredkin, E.: An informational process based on reversible universal cellular automata. Phys. D: Nonlinear Phenom. 45(1–3), 254–270 (1990)MathSciNetCrossRef

12.

Willson, S.J.: Calculating growth rates and moments for additive cellular automata. Discrete Appl. Math. 35(1), 47–65 (1992)MathSciNetCrossRef

13.

Wang, X., Luan, D.: A novel image encryption algorithm using chaos and reversible cellular automata. Commun. Nonlinear Sci. Numer. Simul. 18(11), 3075–3085 (2013)MathSciNetCrossRef

Title: Fractal Arrangement for 2D Cellular Automata and Its Implementation for Outer-Totalistic Rules
Authors: Yoshihiko Kayama
Yuka Koda
Ikumi Yazawa
Publisher: Springer International Publishing
Book: Cellular Automata
Print ISBN: 978-3-319-99812-1

Electronic ISBN: 978-3-319-99813-8

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-99813-8_30

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner