671 research outputs found

### Randomized Cellular Automata

We define and study a few properties of a class of random automata networks.
While regular finite one-dimensional cellular automata are defined on periodic
lattices, these automata networks, called randomized cellular automata, are
defined on random directed graphs with constant out-degrees and evolve
according to cellular automaton rules. For some families of rules, a few
typical a priori unexpected results are presented.Comment: 13 pages, 7 figure

### Conservation Laws in Cellular Automata

If X is a discrete abelian group and B a finite set, then a cellular
automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts.
If g is a real-valued function on B, then, for any b in B^X, we define G(b) to
be the sum over all x in X of g(b_x) (if finite). We say g is `conserved' by F
if G is constant under the action of F. We characterize such `conservation
laws' in several ways, deriving both theoretical consequences and practical
tests, and provide a method for constructing all one-dimensional CA exhibiting
a given conservation law.Comment: 19 pages, LaTeX 2E with one (1) Encapsulated PostScript figure. To
appear in Nonlinearity. (v2) minor changes/corrections; new references added
to bibliograph

### Probabilistic cellular automata with conserved quantities

We demonstrate that the concept of a conservation law can be naturally
extended from deterministic to probabilistic cellular automata (PCA) rules. The
local function for conservative PCA must satisfy conditions analogous to
conservation conditions for deterministic cellular automata. Conservation
condition for PCA can also be written in the form of a current conservation
law. For deterministic nearest-neighbour CA the current can be computed
exactly. Local structure approximation can partially predict the equilibrium
current for non-deterministic cases. For linear segments of the fundamental
diagram it actually produces exact results.Comment: 17 pages, 2 figure

### 5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

We study two-dimensional rotation-symmetric number-conserving cellular
automata working on the von Neumann neighborhood (RNCA). It is known that such
automata with 4 states or less are trivial, so we investigate the possible
rules with 5 states. We give a full characterization of these automata and show
that they cannot be strongly Turing universal. However, we give example of
constructions that allow to embed some boolean circuit elements in a 5-states
RNCA

### Max-plus analysis on some binary particle systems

We concern with a special class of binary cellular automata, i.e., the
so-called particle cellular automata (PCA) in the present paper. We first
propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic
operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2
and 4-3 are solved exactly and their general solutions are found in terms of
max-plus expressions. Finally, we analyze the asymptotic behaviors of general
solutions and prove the fundamental diagrams exactly.Comment: 24 pages, 5 figures, submitted to J. Phys.

### Estimation of the order parameter exponent of critical cellular automata using the enhanced coherent anomaly method.

The stochastic cellular automaton of Rule 18 defined by Wolfram [Rev. Mod.
Phys. 55 601 (1983)] has been investigated by the enhanced coherent anomaly
method. Reliable estimate was found for the $\beta$ critical exponent, based on
moderate sized ($n \le 7$) clusters.Comment: 6 pages, RevTeX file, figure available from [email protected]

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