Life without bounds: does the game of life exhibit self-organized criticality in the thermodynamic limit?

Life without bounds: does the game of life exhibit self-organized criticality in the thermodynamic limit?. Blok, H. J. (. .

Paper abstract bibtex

Recently, a class of phenomena known as self-organized criticality (SOC) has been discovered. SOC is characterized by two properties: firstly, the system exhibits power law behavior typical of a critical state, with no characteristic time or length scales; and secondly, this state is approached naturally, without tuning any external parameters. Early studies explained SOC in terms of conserved quantities [1,2]. Then Bak et al. [3] suggested that the Game of Life, GL, a cellular automaton lacking any conserved quantities, also exhibited SOC. This sparked a debate as to whether GL truly is SOC; conflicting data suggested it was subcritical [4,5,6]. In this paper I explore both sides of the argument in an attempt to resolve the issue. By finding an explicit form for the scaling function the opposing arguments are reconciled and, with some slight reservations, GL is judged to be subcritical. The differences between the analysis herein and other studies is highlighted. I also introduce the reader to some other interesting features of GL, and cellular automata in general, in order to elicit the proper respect for these simple yet complex models. In doing so I hope to impress upon the reader the insufficiencies of the available analytical tools. New methods are required to account for the long-range correlations which develop in GL and other deterministic automata.

@online{blok_life_1995,
	title = {Life without bounds: does the game of life exhibit self-organized criticality in the thermodynamic limit?},
	url = {https://circle.ubc.ca/handle/2429/4037},
	shorttitle = {Life without bounds},
	abstract = {Recently, a class of phenomena known as self-organized criticality ({SOC}) has been
discovered. {SOC} is characterized by two properties: firstly, the system exhibits power law
behavior typical of a critical state, with no characteristic time or length scales; and
secondly, this state is approached naturally, without tuning any external parameters. Early
studies explained {SOC} in terms of conserved quantities [1,2]. Then Bak et al. [3]
suggested that the Game of Life, {GL}, a cellular automaton lacking any conserved
quantities, also exhibited {SOC}. This sparked a debate as to whether {GL} truly is {SOC};
conflicting data suggested it was subcritical [4,5,6].
In this paper I explore both sides of the argument in an attempt to resolve the
issue. By finding an explicit form for the scaling function the opposing arguments are
reconciled and, with some slight reservations, {GL} is judged to be subcritical. The
differences between the analysis herein and other studies is highlighted.
I also introduce the reader to some other interesting features of {GL}, and cellular
automata in general, in order to elicit the proper respect for these simple yet complex
models. In doing so I hope to impress upon the reader the insufficiencies of the available
analytical tools. New methods are required to account for the long-range correlations
which develop in {GL} and other deterministic automata.},
	version = {1327},
	type = {Electronic Thesis or Dissertation},
	author = {Blok, Hendrik J. (Rik)},
	urldate = {2012-02-21},
	date = {1995-11},
	keywords = {Rik's work}
}

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