Abstract
Stephen Wolfram declared computer experiments with pattern formation of cellular automata as “new kind of science” (NKS). It is obviously a great merit of NKS to highlight the experimental approach in the computational sciences [26]. But we claim that even in the future quasi-empirical computer experiments are not sufficient [12]. Cellular automata must be considered complex dynamical systems in the strictly mathematical sense with corresponding equations and proofs. In short, we also need analytical models of cellular automata, in order to find precise answers and predictions in the universe of cellular automata. In this sense, our approach goes beyond Wolfram’s NKS.
An erratum for this chapter can be found at http://dx.doi.org/10.1007/978-3-642-35482-3_24
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-642-35482-3_24
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References
Alligood, K.T., Sauer, T.D., Yorke, J.A.: Chaos: An Introduction to Dynamical Systems. Springer, New York (1996)
Chua, L.O.: CNN: A Paradigm for Complexity. World Scientific, Singapore (1998)
Chua, L.O., Yoon, S., Dogaru, R.: A nonlinear dynamics perspective of Wolfram’s new kind of science. Part I: Threshold of complexity. International Journal of Bifurcation and Chaos (IJBC) 12(12), 2655–2766 (2002)
Chua, L.O., Sbitnev, V.I., Yoon, S.: A nonlinear dynamics perspective of Wolfram’s new kind of science. Part II: Universal neuron. International Journal of Bifurcation and Chaos (IJBC) 13(9), 2377–2491 (2003)
Chua, L.O., Sbitnev, V.I., Yoon, S.: A nonlinear dynamics perspective of Wolfram’s new kind of science. Part III: Predicting the unpredictable. International Journal of Bifurcation and Chaos (IJBC) 14, 3689–3820 (2004)
Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London A 400, 97–117 (1985)
Hoekstra, A.G., Kroc, J., Sloot, P.M.A. (eds.): Simulating Complex Systems by Cellular Automata. Springer, Berlin (2010)
Mainzer, K.: Symmetries of Nature. De Gruyter, New York (1996) (German 1988: Symmetrien der Natur. De Gruyter, Berlin)
Mainzer, K.: Symmetry and Complexity: The Spirit and Beauty of Nonlinear Science. World Scientific, Singapore (2005)
Mainzer, K.: Thinking in Complexity. The Computational Dynamics of Matter, Mind, and Mankind, 5th edn. Springer, Berlin (2007)
Mainzer, K. (ed.): Complexity. European Review (Academia Europaea) 17(2), 219–452 (2009)
Mainzer, K., Chua, L.O.: The Universe as Automaton. From Simplicity and Symmetry to Complexity. Springer, Berlin (2011)
Martin, B.: A universal cellular automaton in quasi-linear time and its S-m-n form. Theoretical Computer Science 123, 199–237 (1994)
Rendell, P.: A Turing machine in Conway’s Game of Life, extendable to a universal Turing machine. In: Adamatzky, A. (ed.) Collision-Based Computing. Springer, New York (2002)
Shilnikov, L., Shilnikov, A., Turaev, D., Chua, L.: Methods of Qualitative Theory in Nonlinear Dynamics I-II. World Scientific, Singapore (1998-2001)
Speiser, A.: Die Theorie der Gruppen von endlicher Ordnung, 4th edn. Birkhauser, Basel (1956)
Turing, A.M.: On computable numbers with an application to the Entscheidungs problem. Proceeedings of the London Mathematical Society 2(42), corrections, ibid 43, 544–546 (1936-1937)
Wolfram, S.: A New Kind of Science. Wolfram Media, Inc., Champaign Il (2002)
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Mainzer, K., von Linde-Akademie, C. (2013). Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System. In: Zenil, H. (eds) Irreducibility and Computational Equivalence. Emergence, Complexity and Computation, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35482-3_5
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