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 |
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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.
In: Physica D: Nonlinear Phenomena, Vol. 202, No. 1-2, 01.03.2005, p. 71-94.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
AN - SCOPUS:14944376681
VL - 202
SP - 71
EP - 94
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1-2
ER -