Do you have (not trivial) examples of a natural phenomenon that illustrates perfectly a mathematical concept, structure, equation or theory ? As suggested by sigoldberg1, I search physical situations in which the underlying mathematics is especially clear. This could be a second separate question: Do you have an example of a natural phenomenon that directly inspired a mathematical theory? do you have pictures ? movies ?

Nautilus Shell (this illustrates Fibonacci?) http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

Fractal coast (this illustrates self similarity): http://www.flickr.com/photos/buggs_moran/4516938146/