One of the defining features of space as we normally experience it is a certain locality that leads most things that happen at some particular position to be able at first to affect only things very near them.
Such locality is built into the basic structure of systems like cellular automata. For in such systems the underlying rules allow the color of a particular cell to affect only its immediate neighbors at each step. And this has the consequence that effects in such systems can spread only at a limited rate, as manifest for example in a maximum slope for the edges of patterns like those in the pictures below.
In physics there also seems to be a maximum speed at which the effects of any event can spread: the speed of light, equal to about 300