### 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 language | English |
---|---|

Pages (from-to) | 71-94 |

Number of pages | 24 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 202 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2005 Mar 1 |

Externally published | Yes |

### Fingerprint

### 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

**Autonomous indefiniteness versus external indefiniteness : Theory of weak topped ∩-structure and its application to elementary local cellular automaton.** / Haruna, Taichi; Gunji, Yukio.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Autonomous indefiniteness versus external indefiniteness

T2 - Theory of weak topped ∩-structure and its application to elementary local cellular automaton

AU - Haruna, Taichi

AU - Gunji, Yukio

PY - 2005/3/1

Y1 - 2005/3/1

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.

KW - Closure operator

KW - Indefiniteness

KW - Local cellular automaton

KW - Open limit

KW - Self-organized criticality

KW - Weak topped ∩-structure

UR - http://www.scopus.com/inward/record.url?scp=14944376681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14944376681&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2005.01.020

DO - 10.1016/j.physd.2005.01.020

M3 - Article

VL - 202

SP - 71

EP - 94

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -