Nonlinear Systems. Part II

Abstract

Patterns pervade the world of nature as well as the world of the intellect. In the biological realm we are quite familiar with the stripes on a zebra, the spots on a leopard, and the colorful markings of certain birds, fish, and butterflies. In the physical world we may have noticed the pretty fringe patterns which occur when thin films of oil spread on a road surface or the wonderful shapes that ice crystals can assume when trees are coated after an ice storm. If we go into a wallpaper shop, we can be overwhelmed by the wide variety of patterns available, the patterns created by someone’s artistic imagination. If we talk to a scientist we will soon find that his or her goal in life is usually to discover (impose?) some underlying pattern to the phenomena under investigation and then attempt to mathematically model that pattern. In this section, we shall look at some attempts to understand or create patterns through the use of nonlinear modeling and concepts. Our first example is from the world of chemistry.

But you will ask, how could a uniform chaos, coagulate at first irregularly in heterogeneous viens as masses to cause hills---Tell me the cause of this, and the answer will perhaps serve for the chaos.

Isaac Newton (1642–1727)