Next: About this document
Up: What Has and What
Previous: Conclusion
References
- 1
-
Jürgen Albert and Karel Culik II, ``A Simple Universal Cellular
Automaton and its One-Way and Totalistic Version,'' Complex Systems
1 1-16 (1987).
- 2
-
Stan Augarten, Bit by Bit, Ticknor and Fields, New York, 1984
(ISBN 0-89919-302-1).
- 3
-
Charles Babbage, Charles Babbage and his Calculating Engines,
(Philip and Emily Morrison, eds.), Dover Publications, Inc., New York,
1961.
- 4
-
R. C. Backhouse and B. A. Carré, ``Regular Algebra Applied to
Path-finding Problems,'' Journal of the Institute of Mathematics
and its Applications, 15 161-186 (1975).
- 5
-
Carter Bays, ``The game of three dimensional life'' (11/20/86) unpublished
(available as a supplement to A. K. Dewdney's February 1987 column).
- 6
-
Carter Bays, ``Candidates for the Game of Life in Three Dimensions,''
Complex Systems 1 373-400 (1987).
- 7
-
Carter Bays, ``Patterns for Simple Cellular Automata in a Universe of
Dense-Packed Spheres,'' Complex Systems 1 853-875 (1987).
- 8
-
Carter Bays, ``Classification of Semitotalistic Cellular Automata in
Three Dimensions,'' Complex Systems 1 373-400 (1987).
- 9
-
Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy, Winning
Ways for your Mathematical Plays, Academic Press, 1982 (ISBN
0-12-091152-3) vol. 2, chapter 25.
- 10
-
Abraham Berman and Robert J. Plemmons, Nonnegative Matrices in the
Mathematical Sciences, Academic Press, New York, 1979 (ISBN
0-12-092250-9).
- 11
-
Janusz A. Brzozowski, ``Derivatives of regular expressions,'' Journal
of the Association for Computing Machinery 11 481-494 (1964).
- 12
-
David J. Buckingham, ``Some facts of life,'' Byte vol. 3, no. 12
(December, 1978), pp. 54-67.
- 13
-
Arthur W. Burks (editor), Essays on Cellular Automata, University of
Illinois Press, Urbana, 1970.
- 14
-
Gerardo Cisneros and Harold V. McIntosh, Notas sobre los lenguajes
REC y Convert (Spanish), Universidad Autonoma de Puebla, 1986.
- 15
-
E. F. Codd, Cellular Automata, Academic Press, New York, 1968.
- 16
-
J. H. Conway, Regular Algebra and Finite Machines, Chapman and
Hall, Ltd., London, 1971 (ISBN 412-10620-5).
- 17
-
Karel Culick II and Sheng Yu, ``Undecidability of CA Classification
Schemes,'' Complex Systems 2 177-190 (1988).
- 18
-
Karel Culick II, Jan Pachl, and Sheng Yu, ``On the Limit Sets of
Cellular Automata,'' SIAM Journal on Computing 18 831-842
(1989).
- 19
-
Predrag Cvitanovic, ``Invariant measurement of strange sets in terms of
cycles,'' (preprint).
- 20
-
A. K. Dewdney, ``Computer Recreations - Building computers in one
dimension sheds light on irreducibly complicated phenomena,''
Scientific American, May 1985, pp. 10-16.
- 21
-
A. K. Dewdney, ``Computer Recreations - The game Life acquires some
successors in three dimensions,'' Scientific American, February
1987, pp 8-13.
- 22
-
A. K. Dewdney, The Armchair Universe, W. H. Freeman and Company,
New York, 1988. (ISBN 0-7167-1939-8 pbk)
- 23
-
A. K. Dewdney, ``Computer Recreations - A cellular universe of debris,
droplets, defects, and demons,'' Scientific American, August
1989, pp 88-91.
- 24
-
M. Dresden and D. Wong, ``Life Games and Statistical Models,''
Proceedings of the National Academy of Sciences (U.S.A.) 72
956-960 (1975).
- 25
-
Manfred Eigen, ``Abstract: The Hypercycle: A Principle of Natural
Self-Organization,'' International Journal of Quantum Chemistry,
Quantum Biology Symposium 5 219 (1978).
- 26
-
Glen Fleck (Ed.), A Computer Perspective, Harvard University
Press, Cambridge, 1973 (ISBN 674-15625-0).
- 27
-
F.R. Gantmacher, The Theory of Matrices, volume 2, Chelsea
Publishing Company, New York, 1959.
- 28
-
Martin Gardner, ``Mathematical Games - The fantastic combinations of John
Conway's new solitaire game `life,' '' Scientific American,
October 1970, pp. 120-123.
- 29
-
Martin Gardner, Wheels, Life, and Other Mathematical Amusements,
W. H. Freeman and Company, New York, 1983. (ISBN 0-7167-1589-9 pbk)
- 30
-
Herman H. Goldstine, The Computer from Pascal to von Neumann,
Princeton University Press, Princeton, 1972 (ISBN 0-691-08104-2).
- 31
-
Solomon W. Golomb, Shift Register Sequences, Holden-Day, Inc., San
Francisco, 1967.
- 32
-
Howard A. Gutowitz, ``Local Structure Theory for Cellular Automata,''
Thesis Rockefeller University, 1987.
- 33
-
Howard A. Gutowitz and Jonathan D. Victor, ``Local structure theory in
more than one dimension,'' Complex Systems 1 57-68 (1987).
- 34
-
Howard A. Gutowitz, Jonathan D. Victor, and Bruce W. Knight, ``Local
structure theory for cellular automata,'' Physica 28D 18-48
(1987).
- 35
-
Howard A. Gutowitz and Jonathan D. Victor, "Local structure theory:
calculation on hexagonal arrays, and interaction of rule and lattice,"
Journal of Statistical Physics 54 495-514 (1989).
- 36
-
Fred Hapgood, ``Let there be Life,'' Omni, vol. 9, no. 7 (April 1987)
pp. 40-46, 116-117.
- 37
-
Brian Hayes, ``Computer Recreations - The cellular automaton offers a
model of the world and a world unto itself,'' Scientific American,
March 1984, pp. 10-16.
- 38
-
Lyman P Hurd, ``Formal Language Characterizations of Cellular Automaton
Limit Sets,'' Complex Systems 1 69-80 (1987).
- 39
-
Lyman P. Hurd, ``The Application of Formal Language Theory to the
Dynamical Behavior of Cellular Automata,'' Thesis, Princeton
University, 1988.
- 40
-
Lyman P Hurd, ``The Non-wandering Set of a CA Map,'' Complex
Systems 2 549-554 (1988).
- 41
-
Erica Jen, ``Global Properties of Cellular Automata,'' Journal of
Statistical Physics 43 219-242 (1986).
- 42
-
Erica Jen, ``Invariant Strings and Pattern-Recognizing Properties of
One-Dimensional Cellular Automata,'' Journal of Statistical
Physics 43 243-265 (1986).
- 43
-
Erica Jen, ``Scaling of preimages in cellular automata,'' Complex
Systems 1 1045-1062 (1987).
- 44
-
Erica Jen, ``Cylindrical cellular automata,'' Communications in
Mathematical Physics 118 569-590 (1988).
- 45
-
S. C. Kleene, "Representation of events in nerve nets and finite
automata," in Claude E. Shannon and John McCarthy (editors),
Automata Studies, Annals of Mathematics Studies #34, Princeton
University Press, Princeton, 1956. (ISBN 0-691-07916-1), pp. 3-41.
- 46
- Christopher G. Langton, ``Self-Reproduction in Cellular
Automata,'' Physica 10D 135-144 (1984).
- 47
- Christopher G. Langton, ``Studying artificial life with
cellular automata,'' Physica 22D 120-149 (1986).
- 48
-
Stephen Levy, Hackers: Heroes of the Computer Revolution, Anchor
Press/ Doubleday, Garden City, New York, 1984 (ISBN 0-385-19195-2),
chapter 7.
- 49
-
O. Martin, A. Odlyzko, and S. Wolfram, ``Algebraic aspects of cellular
automata,'' Communications in Mathematical Physics 93 219-258
(1984).
- 50
-
W. S. McCulloch and W. Pitts, ``A logical calculus of the ideas immanent
in nervous activity,'' Bulletin of Mathematical Biophysics 5
115-133 (1943).
- 51
-
Edward F. Moore, ``Machine models of self-reproduction,'' in A. Burks (ed),
Essays on Cellular Automata, University of Illinois Press, Urbana,
1970. pp. 186-203.
- 52
-
Scott Morris, ``Games - The game of Life,'' Omni, vol. 7, no. 1
(October, 1984), pp. 188-189.
- 53
-
John von Neumann, Theory of Self-reproducing Automata (edited and
completed by A. W. Burks), University of Illinois Press, 1966.
- 54
-
Mark D. Niemiec, ``Life Algorithms,'' Byte vol. 4, no 1 (January,
1979) pp. 90-97.
- 55
-
Norman H. Packard and Stephen Wolfram, ``Two-Dimensional Cellular
Automata,'' Journal of Statistical Physics 38 901-946 (1985).
- 56
-
Kenneth E. Perry, ``Abstract mathematical art,'' Byte, vol. 11,
no. 13 (December 1986), pp. 181-192.
- 57
-
William Poundstone, The Recursive Universe, William Morrow and
Company, New York, 1985 (ISBN 0-688-03975-8).
- 58
-
Kendall Preston, Jr., and Michael J. B. Duff, Modern Cellular
Automata, Plenum Press, New York, 1984 (ISBN 0-306-41737-5).
- 59
-
Anthony Ralston, ``De Bruijn Sequences---A Model Example of the
Interaction of Discrete Mathematics and Computer Science,''
Mathematics Magazine 55 131-143 (1982).
- 60
-
Brian Randell (Ed.), The Origins of Digital Computers: Selected
Papers, Springer Verlag, Berlin, 1973 (ISBN 3-540-06169-X).
- 61
-
D. R. Rutherford, Substitutional Analysis, Edinburgh, at the
University Press (1948).
- 62
-
L.S. Schulman and P.E. Seiden, ``Statistical mechanics of a dynamical
system based on Conway's game of Life,'' Journal of Statistical
Physics 19 293-314 (1978).
- 63
-
Eugene Seneta, Non-Negative Matrices, John Wiley and Sons, New
York, 1973 (ISBN 0-470-77605-6).
- 64
-
Claude E. Shannon and John McCarthy (editors), Automata Studies,
Annals of Mathematics Studies #34, Princeton University Press,
Princeton, 1956. (ISBN 0-691-07916-1).
- 65
-
Alvy Ray Smith III, ``Simple computation-universal cellular spaces,''
Journal of the Association for Computing Machinery 18
339-353 (1971).
- 66
-
Stanislaw Ulam, ``On some mathematical problems connected with patterns of
growth of figures,'' in A. Burks (ed.) Essays on Cellular Automata,
University of Illinois Press, 1970.
- 67
-
Richard S. Varga, Matrix Iterative Analysis, Prentice Hall, Inc,
Englewood Cliffs, New Jersey, (1962).
- 68
-
Robert T. Wainwright (editor), Lifeline, a quarterly newsletter
with 11 issues published between March 1971 and September 1973.
- 69
-
W. John Wilbur, David J. Lipman, and Shihab A. Shamma, ``On the
prediction of local patterns in cellular automata,'' Physica
19D 397-410 (1986).
- 70
-
Stephen Wolfram, ``Statistical mechanics of cellular automata,''
Reviews of Modern Physics 55 601-644 (1983).
- 71
-
Stephen Wolfram, ``Universality and complexity in cellular automata,''
Physica 10D 1-35 (1984).
- 72
-
Stephen Wolfram, ``Computation theory of cellular automata,''
Communications in Mathematical Physics 96 15-57 (1984).
- 73
-
Stephen Wolfram (Ed.), Theory and Applications of Cellular Automata,
World Scientific Press, Singapore, 1986 (ISBN 9971-50-124-4 pbk).
- 74
-
Takeo Yaku, ``The constructibility of a configuration in a cellular
automaton,'' Journal of Computer and System Sciences 7
481-496 (1973).
Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx