Cellular automata with vanishing particles

Authors:
Petr Kůrka
Affiliations:
Faculty of Mathematics and Physics, Charles University in Prague, Malostranské námestí 25, CZ-11800 Praha 1, Czechia
Venue:
Fundamenta Informaticae - Special issue on cellular automata
Year:
2003

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Abstract

We consider particle weight functions which assign weights to certain words. Given a cellular automaton, we search for particle weight functions, for which the total weights of configurations do not increase with time. In this case the weight of a shift-invariant Borel probability measure does not increase either, so we get a Ljapunov function on the space of measures. We give some conditions which ensure that the weight of a measure converges to zero. In particular we prove that this happens in the elementary cellular automaton rule number 18 and in a variant of the Gacs-Kurdyumov-Levin cellular automaton.