Coupled one-dimensional dynamical systems

This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of self-mappings of the unit interval. There is no real mathematics to be found here (in the sense of results stated and proved) and in fact there is an almost complete lack of precise statements. The only thing on offer is the definition of the mappings and a few nice pictures showing examples of their asymptotic limit sets. There is a JavaScript program available, accessible at www.math.uni-bielefeld.de/~preston/iterates.html, which can be used to `discover' more about these mappings. The program might prove to be helpful for anyone interested in doing this.