2015/05/11 by Vladimir Garcı́a-Morales, Garcia-Morales, Vladimir
Computer Science · #Cellular Automata and Applications #Advanced Data Storage Technologies #Algorithms and Data Compression
paper · pdf · doi:10.48550/arxiv.1505.02543
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.