In [M. Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS) 1 (1999), 109–197], Gromov introduces the notion of pre-injective map. Recasting this notion …

An easy question that I have never been able to answer. Suppose we have the CA on $\{ 0,1,2 \}^{\mathbb{N}}$ with local rule given by $f(x,y)=A_{x,y}$ and $A$ the $3\times 3$ matri …

Let's consider a Probabilistic Cellular Automaton on a one dimensional lattice $S$. Each site of the lattice can have two states, $0$ and $1$. The transition probability acting on …

Has the following conjecture been prooved, or has any step in the direction of its proof been done? "ANY Probabilistic Cellular Automata converge fast on the stationary probabilit …

Does there exist a Turing complete, cellular automata with universe and alphabet $\mathbb{Z}$ such that the only allowable configurations are permutations of $\mathbb{Z}$? Formally …

In 2-D lattice random walks by multiple drunks who can't step onto each other, mathematically I would just say the whole cellular automaton updates "at once". But to simulate this …

I have been looking for books on cellular automata, and I really can't afford more than one book right now, so I really need to make the right choice. What would be the right book …

Is there a theory for solving PDE by using Cellular Automata ? Something which is on the line of, passing to the limit (scale) i.e., if you increase the number of grid points the s …

It's an obvious consequence of the pigeonhole principle that any injective function over finite sets is bijective. But there are some similar results in different areas of mathemat …

A little background: As far as I know there is no standard definition of a quantum cellular automaton in the literature. Different authors use different definitions. Here I propose …

I've been drawn to a problem that requires ascertaining the existence of fixed points in the following recurrence relation, any ideas would be much appreciated. I seek neccessary c …

Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for "cellular automata" physics. Google Scholar still gives m …

I'm a little bit hesitant to ask this here, so please notice the tag. My hope is that someone will have a more satisfying answer than what I've heard before... A long time ago I …

Most cellular automata are defined as being updated synchronously. I am interested in asynchronous automata, where they do not all have to update simultaneously. I am restricting …

Does this 2D cellular automaton have a known name and history? n colors (numbered 1 to n), assigned randomly at the start. For each generation, every cell that has at least one n …