منابع مشابه
Transient Behavior of Cellular Automaton Rule 110
The transient behavior of the I-dimensional 2-state 3-input cellular automaton rule 110, one of the simplest "edge of chaos" cellular automata, is investigated numerically. The simulations show that the average transient time Tave increases algebraically with system size N, Tave ~ N"', with a "" 1.08, and that the density of propagating objects (gliders) decays with time as ngl ~ r'Y with I "" ...
متن کاملDynamics of the Cellular Automaton Rule 142
We investigate dynamics of the cellular automaton Rule 142. This rule possesses additive invariant of the second order, namely it conserves the number of blocks “10”. Rule 142 can be alternatively described as an operation on a binary string in which we simultaneously flip all symbols which have dissenting right neighbors. We show that the probability of having a dissenting neighbor can be comp...
متن کاملP-completeness of Cellular Automaton Rule 110
We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is P-complete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polynomial time, this is an exponential improvement on their previously known simulation time overhead.
متن کاملCatalan Numbers and Power Laws in Cellular Automaton Rule 14
We discuss example of an elementary cellular automaton for which the density of ones decays toward its limiting value as a power of the number of iterations n. Using the fact that this rule conserves the number of blocks 10 and that preimages of some other blocks exhibit patterns closely related to patterns observed in rule 184, we derive expressions for the number of n-step preimages of all bl...
متن کاملPersistent Structures in Elementary Cellular Automaton Rule 146
Two types of spacetime structures found in the evolution of rule 146 are presented: very large white triangles, called monoliths, and persistent structures formed by sequential white triangles of even width. The monoliths are discussed in terms of large fluctuations away from equilibrium in a many-body system. The persistent structures are derived by highlighting the nonadditive portions of the...
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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 2014
ISSN: 0385-4035
DOI: 10.14492/hokmj/1416837570