![]() In rule 126, the lengths of the shortest newly excluded blocks on successive steps are 0, 3, 12, 13, 14, 14, 17, 15. And if there are going to be an infinite number of excluded blocks, there must be additional excluded blocks with lengths between n and 2n. If there are n nodes in such a network, then if any blocks are excluded, the shortest one of them must be of length less than n. But whenever the overall behavior is at all complex, there tend to be an infinite set of blocks excluded, making it necessary to use a network of the kind discussed in the main text. In some cases the set of allowed sequences forms a so-called finite complement language (or subshift of finite type) that can be characterized completely just by saying that some finite set of blocks are excluded. Excluded blocks Īs the evolution of a cellular automaton proceeds, the set of sequences that can appear typically shrinks, with progressively more blocks being excluded. Schmidt, Dynamical Systems of Algebraic Origin ( Birkhäuser Verlag, Basel, 1995 ). Ruelle, Thermodynamic Formalism, Encyclopedia of Math and Its Appl 5 ( Addison-Wesley, Reading, Massachussetts, 1978 ). Lecture Note Series 228 ( Cambridge University Press, 1996 ). Schmidt, Ergodic Theory of ℤd Actions, London Math. Sloane, The Encyclopedia of Integer Sequences ( Academic Press, 1995 ). "Maximal measures and entropy for Zν subshifts of finite type," Classical Mechanics and Dynamical Systems (Medford, Mass.), pp. MacDuffie, The Theory of Matrices ( Chelsea, NY, 1956 ). ![]() D. Lind, A Zeta Function for ℤd-Actions, London Math.Marcus, An Introduction to Symbolic Dynamics and Coding ( Cambridge University Press, Cambridge, 1995 ). ![]()
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