|
Preface to Cellular Automata (1984) |
|
The following is a list of some seminal and some survey papers on cellular automata. Most papers on cellular automata cite one or more of the papers listed below, and may therefore be located, for example, through the Science Citation Index.
V. Aladyev, "Survey of research in the theory of homogeneous structures and their applications", Math. Biosci. 22 (1974) 121.
General results on reachability and constructability of classes of configurations in cellular automata.
R.M. Baer and H.M. Martinez, "Automata and Biology", Ann. Rev. Biophys., 3 (1974) 255.
Survey of some properties of cellular automata (mainly computational), and their application to mathematical models in biology.
E.R. Banks, "Information processing and transmission in cellular automata", MIT project MAC report no. TR-81 (1971).
Example and detailed analysis of a simple two-dimensional cellular automaton capable of universal computation.
E.R. Berlekamp, J.H. Conway and R.K. Guy, "Winning Ways for Your Mathematical Plays", Academic Press, Vol. 2, Chapter. 25.
Survey of results on the "Game of Life", an example of a two-dimensional cellular automaton with complex behaviour.
A.W. Burks, "Essays on Cellular Automata", University of Illinois Press (1970).
A collection of several early papers on cellular automata.
E.F. Codd, "Cellular Automata", Academic Press (1968).
Study of a two-dimensional cellular automaton capable of universal computation.
R.L. Dobrushin, V.I. Kryukov and A.L. Toom (editors), "Locally interacting systems and their application in biology", Lecture notes in mathematics, no. 653, Springer-Verlag (1978).
A collection of papers on probabilistic cellular automata.
E. Fredkin, lectures and unpublished work (1965-present).
Studies of structures generated by cellular automata, and their analogy with physics.
M. Gardner, "Wheels, Life and other Mathematical Amusements", Freeman (1983).
A survey of the "Game of Life" (based on several articles in the Mathematical Games section of Scientific American in 1971 and 1972).
G.A. Hedlund, "Endomorphisms and Automorphisms of the Shift Dynamical System", Math. Systems Theor. 3 (1969) 320.
Equivalence of cellular automata to other mathematical systems, together with characterizations of reversible and irreversible classes of cellular automaton rules.
S. Kauffman, "Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets". J. Theor. Biol. 22 (1969) 437.
Study of general properties of random Boolean networks, which may be considered as generalizations of cellular automata, applied to a theory of biological cell types.
O. Martin, A. Odlyzko and S. Wolfram, "Algebraic properties of cellular automata", Bell Laboratories report (1983); to be published in Comm. Math. Phys.
"Exact solutions" for the global properties of a class of cellular automata.
J.C.P. Miller, "Periodic forests of stunted trees", Philos. Trans. R. Soc., Ser A 266 (1970) 63.
Analysis of properties of some additive cellular automata, with applications to number theory. (Elementary account given in C. Sutton, "Forests and numbers and thinking backwards", New Sci. 90 (1981) 209.)
H. Nishio. "A classified bibliography on cellular automata theory (with focus on recent Japanese references)", Proc. Int. Symp. of Unif. Struct. Autom. and Logic. Tokyo (August 21-23, 1975), p. 206 [Available from IEEE, cat. no. 75 CH1052-OC, New York].
A useful but far from complete list of papers on several aspects of cellular automata.
K. Preston et al., "Basics of cellular logic with some applications in medical image processing", Proc. IEEE 67 (1979) 826.
Survey of some applications of two-dimensional cellular automata to image processing, and of machines built to implement them.
G. Rozenberg and A. Salomaa, "The mathematical theory of L systems", Academic Press (1980).
A study of systems related to cellular automata, using methods from formal language theory.
L.S. Schulman and P.E. Seiden, "Statistical Mechanics of a Dynamical System Based on Conway's Game of Life", J. Stat. Phys. 19 (1978) 293.
Study of a two-dimensional cellular automaton in the presence of noise, with possible applications to models of galaxy structure.
A.R. Smith, "Simple computation-universal cellular spaces", J. ACM 18 (1971) 331.
Analysis of the correspondence between one-dimensional cellular automata with many possible values at each site, and computationally-universal Turing machines.
T. Toffoli, "Cellular Automaton Mechanics", PhD Thesis, Logic of Computers Group, University of Michigan (1977).
A systematic study of cellular automata as mathematical systems that incorporate some fundamental physical constraints, including a survey of previous results.
S. Ulam and collaborators, various Los Alamos reports, mostly reprinted in Burkes, op. cit.
Early studies of the generation of complex patterns by simple two-dimensional cellular automata.
J. von Neumann, "Theory of self-reproducing automata", edited by A.W. Burks, Univ. of Illinois press (1966).
Often considered the first work on cellular automata. A study of cellular automata as a mathematical basis for biology, together with an explicit demonstration of self-reproduction in a rather complicated two-dimensional cellular automaton.
S. Wolfram, "Statistical Mechanics of Cellular Automata", Rev. Mod. Phys. 55 (1983) 642.
Discussion of cellular automata as statistical mechanics systems, with extensive references.
S. Wolfram, "Cellular Automata", to be published in Los Alamos Science (fall 1983).
An elementary survey of recent results on cellular automata.
S. Wolfram, "Computation theory of cellular automata". Institute for Advanced Study preprint (November 1983).
Discussion of cellular automata in terms of formal language theory and computation theory.
