127 research outputs found
Universality and Decidability of Number-Conserving Cellular Automata
Number-conserving cellular automata (NCCA) are particularly interesting, both
because of their natural appearance as models of real systems, and because of
the strong restrictions that number-conservation implies. Here we extend the
definition of the property to include cellular automata with any set of states
in \Zset, and show that they can be always extended to ``usual'' NCCA with
contiguous states. We show a way to simulate any one dimensional CA through a
one dimensional NCCA, proving the existence of intrinsically universal NCCA.
Finally, we give an algorithm to decide, given a CA, if its states can be
labeled with integers to produce a NCCA, and to find this relabeling if the
answer is positive.Comment: 13 page
A family of sand automata
We study some dynamical properties of a family of two-dimensional cellular automata: those that arise from an underlying one-dimensional sand automaton whose local rule is obtained using a Latin square. We identify a simple sand automaton Γ whose local rule is algebraic, and classify this automaton as having equicontinuity points, but not being equicontinuous. We also show that it is not surjective. We generalise some of these results to a wider class of sand automata
A Full Computation-relevant Topological Dynamics Classification of Elementary Cellular Automata
Cellular automata are both computational and dynamical systems. We give a
complete classification of the dynamic behaviour of elementary cellular
automata (ECA) in terms of fundamental dynamic system notions such as
sensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but not
chaotic and not eventually weakly periodic. Based on this classification, we
conjecture that elementary cellular automata capable of carrying out complex
computations, such as needed for Turing-universality, are at the "edge of
chaos"
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