ABSTRACT

This chapter presents some patterns involving self-similarity and hyperbolic geometry. It explores some features of the pure reflective systems, obtaining some main features that can be compared with the concepts of geometry. A light ray entering a foamcan reflects and refract chaotically, because of the geometry of the interface of bubbles. The cavity acts as a hyperbolic prism multiplying the scattering of light rays generating patterns related to Poincare disks. The complex pattern observed in the Poincare disk represents a self-similar pattern, in which there is a fine structure at the border of the disk. The physical system constituted by light interacting with foams can give hints for an understanding of collision processes, chaotic dynamics, the scatterers for wireless communications, and the construction of light traps, just to cite a few areas of interest. The observation of light scattering in foams suggested the existence of some dynamics represented by hyperbolic geometry.