  A simple mathematical expression for the universal map for cellular automata
is found in closed form with the help of a digit function, whose most basic
properties are established. This result is found after proving a theorem on the
composition of functions on finite sets. The expression (and the technique used
to obtain it) opens the possibility of gaining mathematical insight in any
cellular automaton rule since it constitutes at the same time a simple and fast
algorithm to implement any such rule.
