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Bibliography

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Cross Ratio

4
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Putzer's Method

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Reversible Automata

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37
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38
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39
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P. Fatou, ``Sur les équations fonctionelles (deuxieme mémoire),'' Bulletin de la Societe Mathematique de France 48 33-94 (1920).

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P. Fatou, ``Sur les équations fonctionelles (troisieme mémoire),'' Bulletin de la Societe Mathematique de France 48 208-314 (1920).

43
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44
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45
Jarkko Kari, ``Reversibility and Surjectivity Problems of Cellullar Automata,'' Journal of Computer and System Sciences 48 149-182 (1994).

46
Jarkko Kari, ``Representation of Reversible Cellular Automata with Block Permutations,'' Mathematical Systems Theory 29 47-61 (1996).

47
D. Koenig, Theorie der endlichen und unendlichen Graphen, Akademische Verlagsgesellschaft, Leipzig, 1936. Reprint: Chelsea Publishing Company, New York.

48
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49
Masakazu Nasu, ``Local Maps Inducing Surjective Global Maps of One Dimensional Tessellation Automata,'' Mathematical Systems Theory 11 327-351 (1978).

50
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51
Stephen Wolfram, ``Universality and complexity in cellular automata,'' Physica 10D 1-35 (1984).

52
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53
Stephen Wolfram (Ed.), Theory and Applications of Cellular Automata, World Scientific Press, Singapore, 1986 (ISBN 9971-50-124-4 pbk).


Chaté-Manneville

54
Bernard Barral, Hugues Chaté and Paul Manneville, ``Collective behaviors in a family of high-dimensional automata,'' Physics Letters A 163 279-285 (1992).

55
R. Bidaux, N. Boccara, and H. Chaté, ``Order of the transition versus space dimension in a family of cellular automata,'' Physical Review A 39 3094-3105 (1989).

81
Jan Hemmingsson, ``A totalistic three-dimensional cellular automaton with quasiperiodic behaviour,'' Physica A 183 255-261 (1992).

57
J. Hemmingsson, A. Sørenson, H. Flyvbjerg and H. J. Herrmann, ``What Synchronization?'' Europhysics Letters 23 629-634 (1993).

71
H. Chaté and P. Manneville, ``Evidence of Collective Behaviour in Cellular Automata,'' Europhysics Letters 14 409-413 (1991).

59
Hugues Chaté and Paul Manneville, ``Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous Updating,'' Progress in Theoretical Physics 87 1-60 (1991).

69
H. Chaté, A. Lemaître, Ph. Marcq, P. Manneville, ``Non-trivial collective behavior in extensively-chaotic dynamical systems: an update,'' Physica A 224 447-457 (1996).

70
Hugues Chaté, Jérôme Losson, ``Non-trivial collective behavior in coupled map lattices: A transfer operator perspective,'' Physica D 103 51-72 (1997).

62
Charles H. Bennett, G. Grinstein, Yu He, C. Jayaprakash and David Mukamel, ``Stability of temporally periodic states of classical many body systems,'' Physical Review A 41 1932-1935 (1990).

63
Roger Bideaux, Nini Boccara and Hugues Chaté, ``Order of transition versus space dimension in a family of cellular automata,'' Physical Review A 39 3094-3105 (1989).

64
P. -M. Binder and V. Privman, ``Second-Order Dynamics in the Collective Temporal Evolution of Complex Systems,'' Physical Review Letters 68 3830-3833 (1992).

65
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66
Tomas Bohr, G. Grinstein, Yu He, and C. Jayaprakash, ``Coherence, Chaos, and Broken Symmetry in Classical, Many-Body Dynamical Systems,'' Physical Review Letters 58 2155-2158 (1987).

67
Hugues Chaté, ``On the analysis of spatiotemporally chaotic data,'' Physica D 86 238-247 (1995).

68
Hugues Chaté, G. Grinstein and Lei-Han Tang, ``Long-Range Correlations in Systems with Coherent (Quasi)periodic Oscillations,'' Physical Review Letters 74 912-915 (1995).

69
H. Chaté, A. Lemaître, Ph. Marcq, P. Manneville, ``Non-trivial collective behavior in extensively-chaotic dynamical systems: an update,'' Physica A 224 447-457 (1996).

70
Hugues Chaté, Jérôme Losson, ``Non-trivial collective behavior in coupled map lattices: A transfer operator perspective,'' Physica D 103 51-72 (1997).

71
H. Chaté and P. Manneville, ``Evidence of Collective Behaviour in Cellular Automata,'' Europhysics Letters 14 409-413 (1991).

72
Hugues Chaté and Paul Manneville, ``Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous Updating,'' Progress of Theoretical Physics 87 1-60 (1991).

73
Hugues Chaté and Paul Manneville, ``Emergence of Effective Low-Dimensional Dynamics in the Macroscopic Behaviour of Coupled Map Lattices,'' Europhysics Letters 17 291-296 (1992).

74
P. Fatou, ``Sur les équations fonctionelles (premiere mémoire),'' Bulletin de la Societe Mathematique de France 47 161-271 (1919).

75
P. Fatou, ``Sur les équations fonctionelles (deuxieme mémoire),'' Bulletin de la Societe Mathematique de France 48 33-94 (1920).

76
P. Fatou, ``Sur les équations fonctionelles (troisieme mémoire),'' Bulletin de la Societe Mathematique de France 48 208-314 (1920).

77
J. A. C. Gallas, P. Grassberger, H.J. Herrmann and P. Ueberholz, ``Noisy collective behaviour in deterministic cellular automata,'' Physica A 180 19-41 (1992).

78
J. Gorodkin, A. Sørensen, and O. Winther, ``Neural Networks and Cellular Automaton Complexity,'' Complex Systems 7 1-24 (1994).

79
G. Grinstein, ``Stability of Nonstationary States of Many-Body Dynamical Systems,'' Journal of Statistical Physics 5 803-815 (1988).

80
Jens M. Houlrick, Itzhak Webman and Mogens H. Jensen, ``Mean field theory and critical behavior of coupled map lattices,'' Physical Review A 41 4210-4222 (1990).

81
Jan Hemmingsson, ``A totalistic three-dimensional cellular automaton with quasiperiodic behaviour,'' Physica A 183 255-261 (1992).

82
J. Hemmingsson and J. Herrmann, ``On Oscillations in Cellular Automata,'' Europhysics Letters 23 15-19 (1993).

83
F. Jiménez-Morales and J. J. Luque, ``Collective behavior of a probabilistic cellular automaton with two absorbing phases,'' Physics Letters A 181 33-38 (1993).

84
Anaël Lemaître, Hugues Chaté, and Paul Manneville, ``Cluster Expansion for Collective Behavior in Discrete-Space Dynamical Systems,'' Physical Review Letters 77 486-489 (1996).

85
Jérôme Losson and Michael C. Mackey, ``Coupled map lattices as models of deterministic and stochastic differential delay equations,'' Physical Review E 52 115-128 (1995).

86
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87
Y. Pomeau, ``Periodic Behavior of Cellular Automata,'' Journal of Statistical Physics 70 1379-1382 (1993).


Rule 110

88
Matthew Cook, ``Introduction to the activity of rule 110'' (copyright 1994-1998 Matthew Cook) http://w3.datanet.hu/ cook/Workshop/CellAut/
Elementary/Rule110/110pics.html

89
Solomon W. Golomb, Polyominoes Charles Scribner's Sons, New York, 1965.

90
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91
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92
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93
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94
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95
W. T. Tutte, Graph Theory As I Have Known It, Clarendon Press, Oxford, 1998 (ISBN 0 19-850251-6).


Lorentz Contraction

96
Serge Lang, $SL_2({\rm R})$, Addison Wesley Publishing Company, Reading, Massachussetts, 1975 (ISBN 0-201-04248-7)

97
V. Bargmann, ``Irreducible unitary representations of the Lorentz group,'' Annals of Mathematics 48 568-640 (1947).

98
E. Wigner, ``On unitary representations of the inhomogeneous Lorentz group,'' Annals of Mathematics 40 149-204 (1939).


Episode I

99
Terry Brooks, Star Wars: Episode I, the Phantom Menace, Ballentine Publishing Company, 1999 (ISBN 0-345-42765-3).

100
David West Reynolds, Star Wars: Episode I, the Visual Dictionary, D. K. Publishing Inc., New York, 1999 (ISBN 0-7894-4701-0).



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2000-03-17