Two well-known ingredients that give rise to the classical phenomenon of chaos are "expansion" and "mixing" of phase-space volumes. The expansion creates exponential divergence between nearby trajectories, and the mixing creates ergodicity of the time evolution. A generic prototype incorporating both ingredients is the Smale horseshoe which acts on a square in phase space, expand it along the unstable direction, contract it along the stable direction, then fold and re-inject it into the original square. In the due process, mixing is created by folding and re-injection, which leads to nonlinear dynamics that displays chaotic motions. However, the original horseshoe was proposed in two dimensions, which leaves us to wonder what would happen if the foldings and re-injections were to take place in multidimensional systems. In this week’s prediction science seminar, we will discuss this generalization using the examples of the coupled Henon map and demonstrate some novel multidimensional phenomena that are otherwise impossible in 2D systems.