The topological skeleton of cellular automaton dynamics

Physica D: Nonlinear Phenomena

Volumn 103, Issue 1-4, 1997, Pages 155-168

  Domain, Christophe ^a   Gutowitz, Howard ^a,b  

^a PSL RESEARCH UNIVERSITY   (France)

^b SANTA FE INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22244488016     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00258-8     Document Type: Article

References (44)

1. C.H. Bennett, in: Emerging Syntheses in the Sciences, ed. D. Pines (Addison-Wesley, Redwood City, 1988);
2. S. Lloyd and H. Pagels, Ann. Phys. 188 (1988) 186.
3. E.R. Berlekamp, J.H. Conway and R.K. Guy, Winning Ways for your Mathematical Plays, Vol. 2, Ch. 25. (Academic Press, New York, 1982).
4. N. Boccara, J. Nasser and M. Roger, Annihilation of defects during the evolution of some one-dimensional class-3 deterministic cellular automata, Europhys. Lett. 13 (6) (1990) 489.
5. N. Boccara, J. Nasser and M. Roger, Particle-like structures and interactions in spatio-temporal patterns generated by one-dimensional deterministic cellular automaton rules, Phys. Rev. A 44 (July 1991).
6. J.P. Crutchfield and J.E. Hanson, Turbulent pattern bases for cellular automata, Physica D 69 (1993) 279-301.
7. J.P. Crutchfield and K. Kaneko, Are attractors relevant to turbulence? Phys. Rev. Lett. 60 (1988) 2715.
8. P. Cvitanović, Invariant measurement of strange sets in terms of cycles, Phys. Rev. Lett. 61 (1988) 2729.
9. M. Denker, Ergodic theory on compact spaces, Lecture Notes in Math. (1976) 527.
10. J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985) 617.
11. M. Eisele, Long-range correlations in chaotic cellular automata, Physica D 48 (1991) 295-310.
12. K. Eloranta, The dynamics of defect ensembles in one-dimensional cellular automata, J. Statist. Phys. 76 (1994) 1377.
13. P. Grassberger, New mechanism for deterministic diffusion, Phys. Rev. A 28 (1983) 3666-3667.
14. P. Grassberger, Chaos and diffusion in deterministic cellular automata, Physica D 10 (1984) 52-58.
15. P. Grassberger, appendix, in: Theory and Applications of Cellular Automata, ed. S. Wolfram (World Scientific, Singapore, 1986).
16. P. Grassberger, Long-range effects in an elementary cellular automaton, J. Statist. Phys. 45 (1986) 27-39.
17. P. Grassberger, Some more exact enumeration results for ID cellular automata, J. Phys. A 20 (1987) 4039-4046.
18. P. Grassberger, Problems in quantifying self-generated complexity, Helv. Phys. Acta 62 (1989) 489.
19. H.A. Gutowitz, Transients, cycles and complexity in cellular automata, Phys. Rev. A 44 (1991) 7881-7884.
20. H.A. Gutowitz, Cryptography with dynamical systems, in: Cellular Automata and Cooperative Phenomena, eds. E. Goles and N. Boccara (Kluwer Academic Press, Dordrecht, MA, 1993).
21. H.A. Gutowitz, J.D. Victor and B.W. Knight, Local structure theory for cellular automata, Physica D 28 (1987) 18-48.
22. J.E. Hanson and J.P. Crutchfield, Computational mechanics of cellular automata: An example, Physica D (1991). these proceedings.
23. E. Jen, Cylindrical cellular automata, Comm. Math. Phys. 118 (1988) 569-590.
24. E. Jen, Aperiodicity in one-dimensional CA, Physica D 45 (1990) 3.
25. E. Jen, Exact solvability and quasiperiodicity of one-dimensional cellular automata, Nonlinearity 4 (2) (1991) 251.
26. K. Kaneko, Attractors, basin structures and information processing in cellular automata, in: Theory and Applications of Cellular Automata, ed. S. Wolfram (World Scientific, Singapore, 1986) pp. 367.
27. W. Li and M. Nordahl, Transient behavior of cellular automata rule 110, Phys. Lett. A 166 (5/6) (1992) 335-339.
28. D.A. Lind, Applications of ergodic theory and sofic systems to cellular automata, Physica D 10 (1984) 36-44.
29. O. Martin, A. Odlyzko and S. Wolfram, Algebraic properties of cellular automata, Comm. Math. Phys. 93 (1984) 219.
30. H.V. McIntosh, Wolfram's class IV automata and a good life, Physica D 45 (1990) 105.
31. W. Meier and O. Staffelbach, Analysis of pseudo random sequences generated by cellular automata, Proc. Eurocrypt'91 (1991) 186-199.
32. A. Sinha and C. Jayaprakash, A numerical study of one-dimensional cellular automata, Physica D 39 (1989) 352-364.
33. C.C. Walker, Attractor dominance patterns in sparsely connected boolean nets, Physica D 45 (1990) 441-451.
34. S. Wolfram, Random sequence generation by cellular automata, Adv. Appl. Math. 7 (1984) 123.
35. S. Wolfram, Universality and complexity in cellular automata, Physica D 10 (1984) 1-35.
36. S. Wolfram, Undecidability and intractability in theoretical physics, Phys. Rev. Lett. 54 (1985) 735.
37. S. Wolfram, Cryptography with cellular automata, Proc. Crypto '85 (1985) pp. 429-432.
38. S. Wolfram, ed., Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986).
39. A. Wuensche, The ghost in the machine:Basins of attraction of random boolean networks, Cognitive Science Research Paper 281, University of Sussex, 1993, in: Artificial Life III, Santa Fe Institute Studies in the Sciences of Complexity (Addison-Wesley, Reading, MA, 1993).
40. A. Wuensche, Complexity in 1-D cellular automata: Gliders, basins of attraction and the Z parameter, Santa Fe Institute working paper 94-04-025 (1994).
41. A. Wuensche, Discrete Dynamics Lab, available from: http://alife.santafe.edu/alife/software/ ddlab.html or ftp://alife.santafe.edu/pub /SOFTWARE/ddlab.
42. A. Wuensche and M. Lesser, The global dynamics of cellular automata, Santa Fe Institute Studies in the Sciences of Complexity, Vol. 1 (Addison-Wesley, Reading, MA, 1992) IBSN 0-201-55740-1.
43. B. Voorhees and S. Bradshaw, Predecessors of cellular automata states III. Garden of Eden classification of cellular automata, Physica D 73 (1994) 152-167.
44. J. Zabolitzky, Critical properties of rule 22 elementary cellular automata, J. Statist. Phys. 50 (1988) 1255.