Digital calculus: Cellular automata dynamics in closed form
arXiv:1505.02543
Abstract
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.
16 pages, 4 figures. Author's note: This preprint is now superseded by arXiv:1507.08455