Multicomputation with Numbers: The Case of Simple Multiway Systems

Abstract

Integer iteration rules such as n |-> {a n + b, c n +d} are studied as minimal examples of the general process of multicomputation. Despite the simplicity of such rules, their multiway graphs can be complex, exhibiting, for example, emergent geometry and difficult questions of confluence. Generalizations to rules involving non-integers and other functions are also considered. Connections with physics and with various number-theoretic and other questions are made.