Abstract
Rule 54, in Wolfram’s notation, is one of elementary yet complexly behaving one-dimensional cellular automata. The automaton supports gliders, glider guns and other non-trivial long transients. We show how to characterize gliders in Rule 54 by diagram representations as de Bruijn and cycle diagrams; offering a way to present each glider in Rule 54 with particular characteristics. This allows a compact encoding of initial conditions which can be used in implementing non-trivial collision-based computing in one-dimensional cellular automata.
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References
Adamatzky, A. (ed.): Collision-Based Computing. Springer, Heidelberg (2003)
Boccara, N., Nasser, J., Roger, M.: Particle like structures and their interactions in spatio-temporal patterns generated by one-dimensional deterministic cellular automaton rules. Physical Review A 44(2), 866–875 (1991)
Golomb, S.W.: Shift Register Sequences. Holden-Day, San Francisco (1967)
Hanson, J.E., Crutchfield, J.P.: Computacional Mechanics of Cellular Automata: An Example. Physics D 103(1-4), 169–189 (1997)
Martínez, G.J., Adamatzky, A., McIntosh, H.V.: Phenomenology of glider collisions in cellular automaton Rule 54 and associated logical gates. Chaos, Solitons and Fractals 28, 100–111 (2006)
Martínez, G.J., McIntosh, H.V., Seck Tuoh Mora, J.C., Chapa Vergara, S.V.: Rule 110 objects and other collision-based constructions. J. Cellular Automata 2(3), 219–242 (2007)
Martínez, G.J., McIntosh, H.V., Seck Touh Mora, J.C., Chapa Vergara, S.V.: Determining a regular language by glider-based structures called phases f i _1 in Rule 110. J. Cellular Automata (in press)
McIntosh, H.V.: Linear cellular automata via de Bruijn diagrams (1991), http://delta.cs.cinvestav.mx/~mcintosh/oldweb/pautomata.html
McIntosh, H.V.: Commentaries on: The Global Dynamics of Cellular Automata (by Wuensche, A., Lesser, M.:) (1993), http://delta.cs.cinvestav.mx/~mcintosh/oldweb/pautomata.html
McIntosh, H.V.: Rule 110 as it relates to the presence of gliders (1999), http://delta.cs.cinvestav.mx/~mcintosh/oldweb/pautomata.html
McIntosh, H.V.: One Dimensional Cellular Automata (by publish)
Voorhees, B.H.: Computational analysis of one-dimensional cellular automata. World Scientific Series on Nonlinear Science, Series A, vol. 15 (1996)
Voorhees, B.H.: Remarks on Applications of De Bruijn Diagrams and Their Fragments. Journal of Cellular Automata (in press)
Wuensche, A., Lesser, M.: The Global Dynamics of Cellular Automata. Santa Fe Institute Studies in the Sciences of Complexity. Addison-Wesley Publishing Company, Reading (1992)
Wolfram, S.: Theory and Aplications of Cellular Automata. World Scientific Press, Singapore (1986)
Wolfram, S.: A New Kind of Science. Wolfram Media, Inc., Champaign (2002)
Wuensche, A.: Classifying Cellular Automata Automatically. Complexity 4(3), 47–66 (1999)
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Martínez, G.J., Adamatzky, A., McIntosh, H.V. (2008). On the Representation of Gliders in Rule 54 by De Bruijn and Cycle Diagrams. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_11
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DOI: https://doi.org/10.1007/978-3-540-79992-4_11
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