K. Lindgren, \Correlations and random information in cellular automata." Complex Systems 1 (1987) 529-543. Home/Search Document Not in Database Summary Related Articles Check |
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Apparent Entropy of Cellular Automata - Martin (Correct)
.... in terms of Kolmogorov complexity, it is obvious that a very simple program is able to build a space time diagram knowing the initial con guration and the transition table (which is nite) A second idea is to consider the evolution of the amount of information of the successive con gurations [10, 14]. But again it is easy to prove that the amount of information cannot grow (if t 1 t 2 then S (t 1 ) A) S (t 2 ) A) where S (t) A) is the entropy of the con guration after t steps, see the de nition below) and contradicts our intuitive idea. Again, this is obvious if we think ....
....(if t 1 t 2 then S (t 1 ) A) S (t 2 ) A) where S (t) A) is the entropy of the con guration after t steps, see the de nition below) and contradicts our intuitive idea. Again, this is obvious if we think of Kolmogorov complexity but let us recall the proof for the metric entropy [10]. De nition 7. Let (A; be a CA and a ergodic measure, the metric entropy of its con guration after t computation steps is de ned as follows: S (t) A) lim n 1 P u2Q n p (t) u log(p (t) u ) n with the usual convention 0 log(0) 0 and where p u is the probability of the ....
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K. Lindgren, \Correlations and Random Information in Cellular Automata, " Complex System, 1 (1987) 529-543.
Complexity of Two-Dimensional Patterns - Lindgren, Moore, Nordahl (2000) (7 citations) Self-citation (Lindgren) (Correct)
....diamond (with n sites along diagonal edges and a total of n 2 (n 1) 2 sites) the number of allowed con gurations is N(n) 2 4n 4 . A more general statement for periodic sets can be made for a class of CA s that form the 2 d analog of the left (right) permutive CA rules studied in e.g. [22, 30, 34] (the ergodic properties of this class of 2 d rules are studied in [59] Proposition. Consider a 2 d CA with neighborhood B associated with a site (0; 0) Say a site in B is extremal if it cannot be written as a convex combination of other points in B. If the transition function f is an injective ....
K. Lindgren, \Correlations and random information in cellular automata." Complex Systems 1 (1987) 529-543.
Complexity of Two-Dimensional Patterns - Lindgren, Moore, Nordahl (1997) (7 citations) Self-citation (Lindgren) (Correct)
....n sites along diagonal edges and a total of n 2 (n Gamma 1) 2 sites) the number of allowed configurations is N(n) 2 4n Gamma4 . A more general statement for periodic sets can be made for a class of CA s that form the 2 d analog of the left (right) permutive CA rules studied in e.g. [19, 25, 29] (the ergodic properties of this class of 2 d rules are studied in [54] Proposition. Consider a 2 d CA with neighborhood B associated with a site (0; 0) Say a site in B is extremal if it cannot be written as a convex combination of other points in B. If the transition function f is an ....
K. Lindgren, "Correlations and random information in cellular automata." Complex Systems 1 (1987) 529--543.
-16 17 -1 - Fig Dislocation (Correct)
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K. Lindgren. Correlations and random information in cellular automata. Complex Systems, 1:529, 1987.
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