A Simple Cellular Automation that Solves the Density and Ordering Problems

Cellular automata (CA) are discrete, dynamical systems that perform computations in a distributed fashion on a spatially extended grid. The dynamical behavior of a CA may give rise to emergent computation, referring to the appearance of global information processing capabilities that are not explicitly represented in the system's elementary components nor in their local interconnections.1 As such, CAs o?er an austere yet versatile model for studying natural phenomena, as well as a powerful paradigm for attaining ?ne-grained, massively parallel computation. An example of such emergent computation is to use a CA to determine the global density of bits in an initial state con?guration. This problem, known as density classi?cation, has been studied quite intensively over the past few years. In this short communication we describe two previous versions of the problem along with their CA solutions, and then go on to show that there exists yet a third version | which admits a simple solution

Parity Problem With A Cellular Automaton Solution

The parity of a bit string of length $N$ is a global quantity that can be efficiently compute using a global counter in ${O} (N)$ time. But is it possible to find the parity using cellular automata with a set of local rule tables without using any global counter? Here, we report a way to solve this problem using a number of $r=1$ binary, uniform, parallel and deterministic cellular automata applied in succession for a total of ${O} (N^2)$ time.Comment: Revtex, 4 pages, final version accepted by Phys.Rev.

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

Invariant Measures and Convergence for Cellular Automaton 184 and Related Processes

For a class of one-dimensional cellular automata, we review and complete the characterization of the invariant measures (in particular, all invariant phase separation measures), the rate of convergence to equilibrium, and the derivation of the hydrodynamic limit. The most widely known representatives of this class of automata are: Automaton 184 from the classification of S. Wolfram, an annihilating particle system and a surface growth model.Comment: 18 page

On Fireflies, Cellular Systems, and Evolware

Many observers have marveled at the beauty of the synchronous flashing of fireflies that has an almost hypnotic effect. In this paper we consider the issue of evolving two-dimensional cellular automata as well as random boolean networks to solve the firefly synchronization task. The task was successfully solved by means of cellular programming based co-evolution performing computations in a completely local manner, each cell having access only to its immediate neighbor's states. An FPGA-based Evolware implementation on the BioWall's cellular tissue and different other simulations show that the approach is very efficient and easily implementable in hardware