Complex Systems

Fractal Replication in Time-manipulated One-dimensional Cellular AutomataDownload PDF

Sugata Mitra
Electronic mail address: SugataM@niit.com

Sujai Kumar
Electronic mail address: sujai@ylog.org
Centre for Research in Cognitive Systems, NIIT Ltd.,
Synergy Building, IIT Campus,
New Delhi 110016, India

Abstract

Properties of elementary one-dimensional cellular automata (CAs) have been studied extensively in the past by varying the number of states each cell can take, the neighborhood of the cell, or the transition rules by which each cell is updated. This paper describes a previously untried variation on a CA system, where each cell is able to anticipate its state one step in the future, and the entire system is allowed to revisit the past over many iterations. Manipulating the time domain in this way allows the CA to exhibit complex fractal replication behavior. Any configuration of active cells can be replicated endlessly while remaining constrained in a self-similar layout.