Cellular Automata and the Concept of Space

After some introductory remarks on space in mathematics and phsyics, an overview of existing applications of cellular automata in physics is given. There are several arguments, partially based on mathematical physics, which impose restrictions on the possible number of dimensions of physical space. One of them claims that our space must have at least three dimensions in order to avoid disturbances between processes of signal transmission. This argument is refuted by means of a cellular-automata model.