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Self-Replication and Cellular Automata

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Encyclopedia of Complexity and Systems Science

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Definition of the Subject

Machine self-replication, besides inspiring numerous fictional books and movies, has long been considered a powerful paradigm to allow artifacts, for example, to survive in hostile environments (such as other planets) or to operate more efficiently by creating populations of machines working together to achieve a given task. Where the self-replication of computing machines is concerned, other motivations can also come into play, related to concepts such as fault tolerance and self-organization.

Cellular automata have traditionally been the framework of choice for the study of self-replicating computing machines, ever since they were used by John von Neumann, who pioneered the field in the 1950s. In this context, self-replication is seen as the process whereby a configuration in the cellular space is capable of creating a copy of itself in a different location.

As a mathematical framework, CA allow researchers to study the mechanisms required to achieve...

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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 entry, the term is extended to account for systems that introduce variations to the basic definition (e.g., 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 entry, 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.

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 entry, by the self-replicating structure).

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 entry 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

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Authors and Affiliations

  1. University of York, York, UK

    Dr. Gianluca Tempesti

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

    Dr. Daniel Mange & Dr. André Stauffer

Authors
  1. Dr. Gianluca Tempesti
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  2. Dr. Daniel Mange
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  3. Dr. André Stauffer
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Corresponding author

Correspondence to Gianluca Tempesti .

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Editors and Affiliations

  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

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Tempesti, G., Mange, D., Stauffer, A. (2013). Self-Replication and Cellular Automata. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-3-642-27737-5_477-7

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_477-7

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