Cellular Automata - Revision history

Admin: Reverted edits by Eboxytezi (Talk) to last version by Jfromm

2011-02-11T21:44:10Z

Reverted edits by Eboxytezi (Talk) to last version by Jfromm

← Older revision		Revision as of 16:44, 11 February 2011
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	locally interacting components.		locally interacting components.

	>== Definition ==		== Definition ==

	A suitable definition of [http://en.wikipedia.org/wiki/Cellular_Automata Cellular Automata] is according to [http://mathworld.wolfram.com/CellularAutomaton.html mathworld] the following statement: ~~"~~A cellular automaton		A suitable definition of [http://en.wikipedia.org/wiki/Cellular_Automata Cellular Automata] is according to [http://mathworld.wolfram.com/CellularAutomaton.html mathworld] the following statement: "A cellular automaton
	is a collection of colored cells on a grid that evolves through a number of discrete time steps according to a set		is a collection of colored cells on a grid that evolves through a number of discrete time steps according to a set
	of rules based on the states of neighboring cells.~~"~~ The two most common neighborhoods in the case of a		of rules based on the states of neighboring cells." The two most common neighborhoods in the case of a
	two-dimensional cellular automaton on a square grid are the		two-dimensional cellular automaton on a square grid are the
	[http://mathworld.wolfram.com/MooreNeighborhood.html Moore neighborhood] (a square neighborhood) and the		[http://mathworld.wolfram.com/MooreNeighborhood.html Moore neighborhood] (a square neighborhood) and the
	[http://mathworld.wolfram.com/vonNeumannNeighborhood.html von Neumann neighborhood] (a diamond-shaped neighborhood).		[http://mathworld.wolfram.com/vonNeumannNeighborhood.html von Neumann neighborhood] (a diamond-shaped neighborhood).

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	== Types ==		== Types ==

Eboxytezi at 00:20, 18 November 2010

2010-11-18T00:20:29Z

← Older revision		Revision as of 19:20, 17 November 2010
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	locally interacting components.		locally interacting components.

	== Definition ==		>== Definition ==

	A suitable definition of [http://en.wikipedia.org/wiki/Cellular_Automata Cellular Automata] is according to [http://mathworld.wolfram.com/CellularAutomaton.html mathworld] the following statement: "A cellular automaton		A suitable definition of [http://en.wikipedia.org/wiki/Cellular_Automata Cellular Automata] is according to [http://mathworld.wolfram.com/CellularAutomaton.html mathworld] the following statement: "A cellular automaton
	is a collection of colored cells on a grid that evolves through a number of discrete time steps according to a set		is a collection of colored cells on a grid that evolves through a number of discrete time steps according to a set
	of rules based on the states of neighboring cells." The two most common neighborhoods in the case of a		of rules based on the states of neighboring cells." The two most common neighborhoods in the case of a
	two-dimensional cellular automaton on a square grid are the		two-dimensional cellular automaton on a square grid are the
	[http://mathworld.wolfram.com/MooreNeighborhood.html Moore neighborhood] (a square neighborhood) and the		[http://mathworld.wolfram.com/MooreNeighborhood.html Moore neighborhood] (a square neighborhood) and the
	[http://mathworld.wolfram.com/vonNeumannNeighborhood.html von Neumann neighborhood] (a diamond-shaped neighborhood).		[http://mathworld.wolfram.com/vonNeumannNeighborhood.html von Neumann neighborhood] (a diamond-shaped neighborhood).

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	== Types ==		== Types ==

Jfromm: /* Types */

2009-01-03T20:53:49Z

Types

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	* IV. Evolution leads to complex localized structures, sometimes long-lived.		* IV. Evolution leads to complex localized structures, sometimes long-lived.

	David Epstein proposed a classification of cellular automaton rules into only three types:		David Epstein proposed a [http://www.ics.uci.edu/~eppstein/ca/wolfram.html classification] of cellular automaton rules into only three types:

	* Contraction impossible		* Contraction impossible

Jfromm at 20:52, 3 January 2009

2009-01-03T20:52:54Z

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 [http://mathworld.wolfram.com/MooreNeighborhood.html Moore neighborhood] (a square neighborhood) and the
 [http://mathworld.wolfram.com/vonNeumannNeighborhood.html von Neumann neighborhood] (a diamond-shaped neighborhood).
 == Applets ==

Jfromm at 15:28, 14 September 2008

2008-09-14T15:28:46Z

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	'''Cellular Automata''' are regular arrays of identical finite state automata whose next state is determined solely by their		'''Cellular Automata''' are regular arrays of identical finite state automata whose next state is determined solely by their
	current state and the state of their neighbours, usually by a boolean transition function. They are closely related to		current state and the state of their neighbours, usually by a boolean transition function. They are closely related to
	[[Random Boolean Network\|~~Randåom~~ Boolean Networks (RBN)]]. A CA contains many cells and each cell is a finite-state automaton		[[Random Boolean Network\|Random Boolean Networks (RBN)]]. A CA contains many cells and each cell is a finite-state automaton
	connected to its neighbors - and so the whole machine or device is called a cellular automaton (pl. cellular automata). They		connected to its neighbors - and so the whole machine or device is called a cellular automaton (pl. cellular automata). They
	were introduced by the mathematician John von Neumann in the 1950s as simple models of biological self-reproduction, and they		were introduced by the mathematician John von Neumann in the 1950s as simple models of biological self-reproduction, and they

Jfromm: New page: '''Cellular Automata''' are regular arrays of identical finite state automata whose next state is determined solely by their current state and the state of their neighbours, usually by a ...

2008-09-14T15:28:19Z

New page: '''Cellular Automata''' are regular arrays of identical finite state automata whose next state is determined solely by their current state and the state of their neighbours, usually by a ...

New page

'''Cellular Automata''' are regular arrays of identical finite state automata whose next state is determined solely by their
current state and the state of their neighbours, usually by a boolean transition function. They are closely related to
[[Random Boolean Network|Randåom Boolean Networks (RBN)]]. A CA contains many cells and each cell is a finite-state automaton
connected to its neighbors - and so the whole machine or device is called a cellular automaton (pl. cellular automata). They
were introduced by the mathematician John von Neumann in the 1950s as simple models of biological self-reproduction, and they
are elementary models for [[Complex System|complex systems]] and processes consisting of a large number of simple, homogeneous,
locally interacting components.

== Definition ==

A suitable definition of [http://en.wikipedia.org/wiki/Cellular_Automata Cellular Automata] is according to [http://mathworld.wolfram.com/CellularAutomaton.html mathworld] the following statement: "A cellular automaton
is a collection of colored cells on a grid that evolves through a number of discrete time steps according to a set
of rules based on the states of neighboring cells." The two most common neighborhoods in the case of a
two-dimensional cellular automaton on a square grid are the
[http://mathworld.wolfram.com/MooreNeighborhood.html Moore neighborhood] (a square neighborhood) and the
[http://mathworld.wolfram.com/vonNeumannNeighborhood.html von Neumann neighborhood] (a diamond-shaped neighborhood).

== Applets ==

Good Cellular Automata applets, including 1-dimensional CA and 2-dimensional CA where you can edit the rules online, can be found at the site [http://www.sussex.ac.uk/space-science/ca.html]. Rules with complex patterns are for instance Wolfram's [http://mathworld.wolfram.com/Rule30.html Rule 30] and or [http://mathworld.wolfram.com/Rule110.html Rule 110]. Mirek's Java Cellebration [http://psoup.math.wisc.edu/mcell/mjcell/mjcell.html MJCell] is a Java applet that allows playing 300+ Cellular Automata rules and 1400+ patterns. It can play rules from 13 CA rules families. A nice tutorial from David J. Eck about Cellular Automata and "the edge of chaos" can be found [http://math.hws.edu/xJava/CA/index.html here].

== Game of Life ==

[http://en.wikipedia.org/wiki/Conway's_Game_of_Life Conway's Game of Life] is one of the most popular two-dimensional CA.
It was invented by John H. Conway. The rules are very simple:

'''Birth''' If an unoccupied cell has 3 occupied neighbors, it becomes occupied.
'''Survival''' If an occupied cell has 2 or 3 neighbors, the organism survives to the next generation.
'''Death''' If an occupied cell has 0..1 or 4..8 occupied neighbors,
the organism dies (0,1: of loneliness; 4-8: of overcrowding).

A description of the game can be found at the [http://mathworld.wolfram.com/Life.html mathworld] site.

Interactive Website by Paul Callahan: [http://www.math.com/students/wonders/life/life.html What is the Game of Life]

More about Conway's Game of Life :
http://www.tech.org/~stuart/life/rules.html

Interactive Essay: Exploring Emergence [http://llk.media.mit.edu/projects/emergence/life-intro.html The Facts of Life]

John Conway's Game of Life - Applet by Edwin Martin
[http://www.bitstorm.org/gameoflife/]

John Conway's Game of Life - Applet by Alan Hensel
[http://www.ibiblio.org/lifepatterns/]

== Larger than Life ==

Available in MJCell: Larger than Life
(an extension of the Game of Life to a larger radius or diameter)
[http://psoup.math.wisc.edu/mcell/mjcell/mjcell.html]

== Scientists ==

[http://en.wikipedia.org/wiki/Stephen_Wolfram Stephen Wolfram] is the author
of the computer program Mathematica, the founder of Wolfram Research, and mainly
known for his work about cellular automata.
Andrew Ilachinski works for the [http://www.cna.org/ Center for Naval Analyses (CNA)], USA.

Tommaso Toffoli is a Professor in the Electrical and Computer Engineering Department at Boston University. He has done a lot of work about Cellular Automata (CA), and a large parts of his CA work resembles Stephen Wolfram's and Edward Fredkin's approach to understand physical systems trough CA simulations. Some Publications can be found [http://pm1.bu.edu/~tt/publ.html here].

== References ==

* [http://cscs.umich.edu/~crshalizi/notebooks/cellular-automata.html C.R. Shalizi's Notebook Entry on CA]
* [http://mathworld.wolfram.com/CellularAutomaton.html Mathworld Entry for CA]
* [http://en.wikipedia.org/wiki/Cellular_automaton Main Wikipedia Entry for CA]
* [http://en.wikipedia.org/wiki/Conway's_Game_of_Life Main Wikipedia Entry for Conway's Game of Life]

== Books ==

There are two major books on Cellular Automata:

* Stephen Wolfram, ''A new kind of science'', Wolfram Media, Inc., 2002 [http://www.wolframscience.com/nksonline]
* Andrew Ilachinski, ''Cellular Automata: A Discrete Universe'', World Scientific, 2001, ISBN 9810246234

Other, less popular books:

* Tommaso Toffoli and Norman Margolus, ''Cellular Automata Machines: A New Environment for Modeling'', MIT Press, 1987, ISBN 0262200600
* Howard Gutowitz (editor), ''Cellular Automata: Theory and Experiment'', MIT Press, 1990, ISBN 0262570866