Autocatalytic systems, which abound in chemistry and biology, are examples of nonlinear systems. The most familiar example of this type of behaviour is the complex spiral pattern observed in the BZ (Belousov-Zhabotinsky) reaction.
Golden ratio: The Golden Ratio is a term (with an astounding number of aliases, including Golden Section and Golden Mean) used to describe aesthetically pleasing proportioning within a piece. However, it is not merely a term -- it is an actual ratio.
A Curled Millipede looks like a beautiful curl.Exhibiting its main defense mechanism, a millipede curls into a tight spiral. In this fashion it protects its legs—on average between 100 and not the thousand its name suggests—inside its body.