# Emergent phenomena in large sparse random arrays of Conway's 'Game of Life'

@article{Gotts2000EmergentPI, title={Emergent phenomena in large sparse random arrays of Conway's 'Game of Life'}, author={Nicholas Mark Gotts}, journal={International Journal of Systems Science}, year={2000}, volume={31}, pages={873 - 894} }

This paper describes some well-defined types of emergence that occur in a class of large, initially random arrays of a well-known binary cellular automaton, Conway's 'Game of Life'. Results concerning the existence or non-existence of finite patterns with particular properties are used to advance the global analysis. It is shown that in infinite (and very large finite) arrays of the Game of Life with initially sparse and randomly distributed non-uniformities, self-organized construction…

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## References

SHOWING 1-10 OF 28 REFERENCES

Nonlinear dynamics of the cellular-automaton "game of Life"

- Physics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1993

A statistical analysis of the «game of Life» due to Conway is reported, based on extensive computer simulations starting with uncorrelated distributions of live sites at t=0.

Self-organized criticality in the 'Game of Life"

- Nature
- 1989

THE 'Game of Life'1,2 is a cellular automaton, that is, a lattice system in which the state of each lattice point is determined by local rules. It simulates, by means of a simple algorithm, the…

On the game of life: population and its diversity

- Mathematics
- 1993

Abstract One of the most important features of biological life in all levels is its astounding diversity. In this work we study the well-known game “Life” due to Conway analysing the statistics of…

Self-replicating structures in a cellular automata space

- Mathematics, Computer Science
- 1996

This article demonstrates for the first time that it is possible to create cellular automata models in which a self-replicating structure emerges from an initial state having a random density and distribution of individual components.

Tight Bounds on Periodic Cell Configurations in Life

- Mathematics, Computer ScienceExp. Math.
- 1998

Three explicit methods are presented to construct oscillators in Conway's Life while guaranteeing certain complexity bounds, leading to the existence of an infinite sequence of oscillators of periods n = 58, 59, 60, … and uniformly bounded population.

'Life' not critical?

- PhysicsNature
- 1991

SIR - Bak et al. have presented evidence that the cellular automaton, the 'game of life', develops into a self-organized critical state, characterized by a D(T)^(-1.6) distribution of times T…

Some New Facts of Life

- Mathematics
- 1998

We investigate the asymptotic density of living cells as dependent on an initial density, the results of scattering of gliders on small stable configurations and the damage spreading in an open…

Computational mechanics of cellular automata: an example

- Mathematics
- 1997

We illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space-time behavior of elementary one-dimensional cellular automaton rule 54. The…

Role of initial conditions in the classification of the rule space of cellular automata dynamics.

- Mathematics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

This work describes the embedding of a "small" universal turing machine, due to Minski, into a cellular automaton rule table and shows that the identification of the Wolfram class depends crucially on the set of initial conditions used to simulate the given CA.

Cellular automata with almost periodic initial conditions

- 1994

Cellular automata are dynamical system on the compact metric space of subshifls. They leave many classes of sukhifts invariant. Here we show that c e l l u l ~ automata leave 'circle subhhifls'…