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Self-Replication and Cellular Automata

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Computational Complexity

Article Outline

Glossary

Definition of the Subject

Introduction

Von Neumann's Universal Constructor

Self‐Replication for Artificial Life

Other Approaches to Self‐Replication

Future Directions

Bibliography

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Abbreviations

Cellular automaton:

A cellular automaton (CA) is a mathematical framework modeling an array of cells that interact locally with their neighbors. In this cellular space, each cell has a set of neighbors, cells have values or states, all the cells update their values simultaneously at discrete time steps or iterations, and the new state of a cell is determined by the current state of its neighbors (including itself) according to a local function or rule, identical for all cells. In the article, the term is extended to account for systems that introduce variations to the basic definition (for example, systems where cells do not update simultaneously or do not have the same set of rules in every cell).

Following the historical pattern, in the article the same term is also used to refer to an object or structure built within the cellular space, i. e., a set of cells in a particular, usually active, state (overlapping with the definition of Configuration).

Configuration:

A set of cells in a given state at a given time. Usually, but not always, the term refers to the state of all the cells in the entire space. The initial configuration is the state of the cells at time \( { t=0 } \).

Self‐replication:

The process whereby a cellular automaton configuration creates a copy of itself in the cellular space. Incidentally, you will note that in the article we use the terms self‐replication and self‐reproduction interchangeably. In reality, the two terms are not really synonyms: self‐reproduction is more properly applied to the reproduction of organisms, while self‐replication concerns the cellular level. The more correct term to use in most cases would probably be self‐replication, but since von Neumann favored self‐reproduction, we will ignore the distinction.

Self‐reproduction:

See Self‐Replication

Construction:

The process that occurs when one or more cells, initially in the inactive or quiescent state are assigned an active state (in the context of this article, by the self‐replicating structure).

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Author information

Authors and Affiliations

  1. University of York, York, UK

    Gianluca Tempesti

  2. Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Daniel Mange & André Stauffer

Authors
  1. Gianluca Tempesti
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  2. Daniel Mange
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  3. André Stauffer
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Tempesti, G., Mange, D., Stauffer, A. (2012). Self-Replication and Cellular Automata. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_172

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