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Cellular automata and the concept of space

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Parallelism, Learning, Evolution (WOPPLOT 1989)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 565))

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Abstract

After some introductory remarks on space in mathematics and phsyics, an overview of existing applications of cellular automata in physics is given. There are several arguments, partially based on mathematical physics, which impose restrictions on the possible number of dimensions of physical space. One of them claims that our space must have at least three dimensions in order to avoid disturbances between processes of signal transmission. This argument is refuted by means of a cellular-automata model.

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References

  • BERLEKAMP, E.R., CONWAY, J.H., GUY, R.K., Winning ways for jour mathematical plays, vol. 2. Academic Press, London 1982

    Google Scholar 

  • BRAITENBERG, V., Vehicles. Experiments in synthetic psychology. MIT Press, Cambridge/Mass. 1984

    Google Scholar 

  • BÜCHEL, W., Philosophische Probleme der Physik. Herder, Freiburg 1965

    Google Scholar 

  • COURANT, R., HILBERT, D., Methods of mathematical physics, vol. 2. Interscience, New York 1962

    Google Scholar 

  • DEMONGEOT, J., GOLES, E., TCHUENTE, M. (eds.), Dynamical systems and cellular automata. Acad. Press, London 1985

    Google Scholar 

  • FARMER, D., TOFFOLI, T., WOLFRAM, S. (eds.), Cellular automata (Proc. Workshop Los Alamos, March 1983). North-Holland, Amsterdam 1984 (= vol. 10 (1984) of Physica D)

    Google Scholar 

  • GERNERT, D., A cellular-space model for studying wave-particle dualism. In: R. TRAPPL (ed.), Cybernetics and systems '86, Reidel, Dordrecht 1986, p. 117–122

    Google Scholar 

  • GERNERT, D., Cellular-space models for processes of measurement. In: R. TRAPPL (ed.), Cybernetics and systems '88, part 1. Kluwer, Dordrecht 1988, p. 109–115

    Google Scholar 

  • HÄNDLER, W., LEGENDI, T., WOLF, G. (eds.) Parcella '84 (Proc. Workshop Berlin, Sept. 1984). Akademie-Verlag, Berlin 1985

    Google Scholar 

  • HOGEWEG, P., Locally synchronised developmental systems. Int.J. General Systems 6 (1980) 57–73

    Google Scholar 

  • HOGEWEG, P., Cellular automata as a paradigm for ecological modelling. Applied Mathematics and Computation 27 (1988) 81–100

    Google Scholar 

  • MANIN, Yu. I., Strings. Math. Intelligencer 11 (1989) 59–65

    Google Scholar 

  • NAAS, J., SCHMID, H.L., Mathematisches Wörterbuch. Akademie-Verlag, Berlin 1961

    Google Scholar 

  • PRESTON, K., DUFF, M. J. B., Modern cellular automata. Plenum Press, New York 1984

    Google Scholar 

  • SNEDDON, I.N. (ed.), Encyclopedic dictionary of mathematics for engineers and applied scientists. Pergamon, Oxford 1976

    Google Scholar 

  • TOFFOLI, T., MARGOLUS, N., Cellular automata machines. MIT Press, Cambridge/Mass. 1987

    Google Scholar 

  • WESTPHAL, W. H., Physik. Springer, Berlin, 14. Aufl. 1950

    Google Scholar 

  • WOLFRAM, S., Preface (to the proceedings volume listed under FARMER). Physica D 10 (1984) vii–xii (1984a)

    Google Scholar 

  • WOLFRAM, S., Cellular automata as models of complexity. Nature 311 (4 Oct. 1984) 419–424 (1984b)

    Google Scholar 

  • WOLFRAM, S., Some recent results and questions about eellular automata. In: DEMONGEOT et al. (eds.) 1984, p. 153–167 (1984c)

    Google Scholar 

  • ZUSE, K., Rechnender Raum. Vieweg, Braunschweig 1969

    Google Scholar 

  • ZUSE, K., Ansätze einer Theorie des Netzautomaten. Nova Acta Leopoldina, N.F., Nr. 220, Bd. 43 (1975) 5–46

    Google Scholar 

  • ZUSE, K., The computing universe. Int. J. of Theoret. Physics 21 (1982) 589–600

    Google Scholar 

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J. D. Becker I. Eisele F. W. Mündemann

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© 1991 Springer-Verlag Berlin Heidelberg

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Gernert, D. (1991). Cellular automata and the concept of space. In: Becker, J.D., Eisele, I., Mündemann, F.W. (eds) Parallelism, Learning, Evolution. WOPPLOT 1989. Lecture Notes in Computer Science, vol 565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55027-5_5

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  • DOI: https://doi.org/10.1007/3-540-55027-5_5

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  • Print ISBN: 978-3-540-55027-3

  • Online ISBN: 978-3-540-46663-5

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