Autonomous indefiniteness versus external indefiniteness: Theory of weak topped ∩-structure and its application to elementary local cellular automaton

Taichi Haruna, Yukio Gunji

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We propose a theory to formalize the indefinite features of living systems in the framework of weak topped ∩-structure. This theory contains two notions of indefiniteness, one is called external indefiniteness and the other is called autonomous indefiniteness. The former is defined as the outside of fixed points of the closure operator and the latter is defined as the difference between the set of fixed points of the weakened closure operator and a given set which defines the closure. This theory is then applied to elementary local cellular automaton (ELCA) in which the time development of its cell is driven by observing the dynamics of its nearest neighbors at the previous time step, followed by taking the closure (or the weak closure) in the appropriate space. The behavior of ELCA is characterized by its algebraic and statistical properties. In particular, we show that self-organized criticality (SOC)-like behavior appears in ELCA driven by the weakened closure operator.

Original languageEnglish
Pages (from-to)71-94
Number of pages24
JournalPhysica D: Nonlinear Phenomena
Volume202
Issue number1-2
DOIs
Publication statusPublished - 2005 Mar 1
Externally publishedYes

Fingerprint

Closure Operator
cellular automata
Cellular automata
Cellular Automata
closures
Closure
Fixed point
Living Systems
Self-organized Criticality
operators
Statistical property
Nearest Neighbor
Cell
cells

Keywords

  • Closure operator
  • Indefiniteness
  • Local cellular automaton
  • Open limit
  • Self-organized criticality
  • Weak topped ∩-structure

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

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abstract = "We propose a theory to formalize the indefinite features of living systems in the framework of weak topped ∩-structure. This theory contains two notions of indefiniteness, one is called external indefiniteness and the other is called autonomous indefiniteness. The former is defined as the outside of fixed points of the closure operator and the latter is defined as the difference between the set of fixed points of the weakened closure operator and a given set which defines the closure. This theory is then applied to elementary local cellular automaton (ELCA) in which the time development of its cell is driven by observing the dynamics of its nearest neighbors at the previous time step, followed by taking the closure (or the weak closure) in the appropriate space. The behavior of ELCA is characterized by its algebraic and statistical properties. In particular, we show that self-organized criticality (SOC)-like behavior appears in ELCA driven by the weakened closure operator.",
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T2 - Theory of weak topped ∩-structure and its application to elementary local cellular automaton

AU - Haruna, Taichi

AU - Gunji, Yukio

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N2 - We propose a theory to formalize the indefinite features of living systems in the framework of weak topped ∩-structure. This theory contains two notions of indefiniteness, one is called external indefiniteness and the other is called autonomous indefiniteness. The former is defined as the outside of fixed points of the closure operator and the latter is defined as the difference between the set of fixed points of the weakened closure operator and a given set which defines the closure. This theory is then applied to elementary local cellular automaton (ELCA) in which the time development of its cell is driven by observing the dynamics of its nearest neighbors at the previous time step, followed by taking the closure (or the weak closure) in the appropriate space. The behavior of ELCA is characterized by its algebraic and statistical properties. In particular, we show that self-organized criticality (SOC)-like behavior appears in ELCA driven by the weakened closure operator.

AB - We propose a theory to formalize the indefinite features of living systems in the framework of weak topped ∩-structure. This theory contains two notions of indefiniteness, one is called external indefiniteness and the other is called autonomous indefiniteness. The former is defined as the outside of fixed points of the closure operator and the latter is defined as the difference between the set of fixed points of the weakened closure operator and a given set which defines the closure. This theory is then applied to elementary local cellular automaton (ELCA) in which the time development of its cell is driven by observing the dynamics of its nearest neighbors at the previous time step, followed by taking the closure (or the weak closure) in the appropriate space. The behavior of ELCA is characterized by its algebraic and statistical properties. In particular, we show that self-organized criticality (SOC)-like behavior appears in ELCA driven by the weakened closure operator.

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KW - Open limit

KW - Self-organized criticality

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