### Abstract

We propose a model based on Elementary Cellular Automata (ECA) where each cell has its own semantics defined by a lattice. Semantics play the following two roles: (1) a state space for computation and (2) a mediator generating and negotiating the discrepancy between the rule and the state. We call semantics playing such roles 'local semantics'. A lattice is a mathematical structure with certain limits. Weakening the limits reveals local semantics. Firstly, we implement local semantics for ECA and call the result 'Lattice-Driven Cellular Automata' (LDCA). In ECA rules are common and invariant for all cells, and uniquely determine the state changes, whereas in LDCA rules and states interplay with each other dynamically and directly in each cell. Secondly, we compare the space-time patterns of LDCA with those of ECA with respect to the relationship between the mean value and variance of the 'input-entropy'. The comparison reveals that LDCA generate complex patterns more universally than ECA. Lastly, we discuss the observation that the direct interplay between levels yields wholeness dynamically.

Original language | English |
---|---|

Pages (from-to) | 187-197 |

Number of pages | 11 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 237 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Feb |

Externally published | Yes |

### Fingerprint

### Keywords

- Cellular automaton
- Hierarchy
- Lattice
- Semantics
- Wholeness

### ASJC Scopus subject areas

- Applied Mathematics
- Statistical and Nonlinear Physics

### Cite this

*Physica D: Nonlinear Phenomena*,

*237*(2), 187-197. https://doi.org/10.1016/j.physd.2007.08.010

**Lattice-driven cellular automata implementing local semantics.** / Uragami, Daisuke; Gunji, Yukio.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 237, no. 2, pp. 187-197. https://doi.org/10.1016/j.physd.2007.08.010

}

TY - JOUR

T1 - Lattice-driven cellular automata implementing local semantics

AU - Uragami, Daisuke

AU - Gunji, Yukio

PY - 2008/2

Y1 - 2008/2

N2 - We propose a model based on Elementary Cellular Automata (ECA) where each cell has its own semantics defined by a lattice. Semantics play the following two roles: (1) a state space for computation and (2) a mediator generating and negotiating the discrepancy between the rule and the state. We call semantics playing such roles 'local semantics'. A lattice is a mathematical structure with certain limits. Weakening the limits reveals local semantics. Firstly, we implement local semantics for ECA and call the result 'Lattice-Driven Cellular Automata' (LDCA). In ECA rules are common and invariant for all cells, and uniquely determine the state changes, whereas in LDCA rules and states interplay with each other dynamically and directly in each cell. Secondly, we compare the space-time patterns of LDCA with those of ECA with respect to the relationship between the mean value and variance of the 'input-entropy'. The comparison reveals that LDCA generate complex patterns more universally than ECA. Lastly, we discuss the observation that the direct interplay between levels yields wholeness dynamically.

AB - We propose a model based on Elementary Cellular Automata (ECA) where each cell has its own semantics defined by a lattice. Semantics play the following two roles: (1) a state space for computation and (2) a mediator generating and negotiating the discrepancy between the rule and the state. We call semantics playing such roles 'local semantics'. A lattice is a mathematical structure with certain limits. Weakening the limits reveals local semantics. Firstly, we implement local semantics for ECA and call the result 'Lattice-Driven Cellular Automata' (LDCA). In ECA rules are common and invariant for all cells, and uniquely determine the state changes, whereas in LDCA rules and states interplay with each other dynamically and directly in each cell. Secondly, we compare the space-time patterns of LDCA with those of ECA with respect to the relationship between the mean value and variance of the 'input-entropy'. The comparison reveals that LDCA generate complex patterns more universally than ECA. Lastly, we discuss the observation that the direct interplay between levels yields wholeness dynamically.

KW - Cellular automaton

KW - Hierarchy

KW - Lattice

KW - Semantics

KW - Wholeness

UR - http://www.scopus.com/inward/record.url?scp=38549093695&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38549093695&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2007.08.010

DO - 10.1016/j.physd.2007.08.010

M3 - Article

AN - SCOPUS:38549093695

VL - 237

SP - 187

EP - 197

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 2

ER -