This article surveys some theoretical aspects of cellular automata CA research. In particular,
we discuss classical and new results on reversibility, conservation laws, limit sets …

Cellular automata are simple models of computation which exhibit fascinatingly complex
behavior. They have captured the attention of several generations of researchers, leading to …

In this chapter we have presented mathematical modeling approaches to biological pattern
formation. While reaction-diffusion models are appropriate to describe the spatio-temporal …

The problem whether a given two-or higher-dimensional cellular automaton is reversible is
shown to be algorithmically undecidable. A cellular automaton is called reversible if it has an …

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from
simple local interaction and computation. Since the inception of cellular automaton (CA) by …

The limit set of a celullar automaton consists of all the configurations of the automaton that
can appear after arbitrarily long computations. It is known that the limit set is never empty—it …

Classification is one of the most important problems in the theory of CA. For instance,
assessing how CA design choices impact the generated dynamics requires an overview of …

Reversible computing is a paradigm where computing models are defined so that they
reflect physical reversibility, one of the fundamental microscopic physical property of Nature …

A cellular automaton is a dynamical system on an infinite array of cells defined by a local
update rule that is applied simultaneously at all cells. By carefully choosing the update rule …

We prove that definitions of number-conserving cellular automata found in literature are
equivalent. A necessary and sufficient condition for cellular automata to be number …