On fundamental diagram of stochastic cellular automata with a quadratic conserved quantity

A Phase Diagram for Elementary Cellular Automata

We construct a phase diagram for the possible dynamics of one-dimensional, two-state, three-neighbor cellular automaton rules, using a new parameter (in conjunction with the previously known activity parameter). The new parameter 'estimates the average sensitivity of rule outcome to small changes in neighborhood configuration.

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 ...

On the decomposition of stochastic cellular automata

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the stochastic cellular automaton evolution. The s...

Hydrodynamics of Stochastic Cellular Automata *

We investigate a stochastic version of cellular automata used for simulating hydrodynamical flows, e. g. the HPP and FHP models. The extra stochasticity consists of "random exchanges" between neighboring cells which conserve momentum. We prove that, in suitable limits, these models satisfy the appropriate continuous Boltzmann and hydrodynamic equations, the same as those conjectured for the ori...

Dynamics of Real Quadratic Cellular Automata