Mandelbrot recognized a self-similar pattern that the fractals formed. He then cross-linked this new geometrical idea with hundreds of examples, from cotton prices to the regularity of the flooding of the Nile River. Mitchell Feigenbaum found the constants or ratios that are responsible for the phase transition state when order turns to chaos. Optics, economics, electronics, chemistry, biology, and psychology quickly used this new analytic tool. Fractal geometry is now being used to graphically show change and evolution in technology, sociology, economics, psychotherapy, medicine, psychology, astronomy, evolutionary theory, and the metaphorical application is spreading to art, humanities, philosophy and theology.
Human history is an excellent example of aperiodic behavior.
Civilization may appear to rise and fall, but things never happen in the same way. Small events or single personalities may change the world around them. The symbolic use of chaos to delineate the interactions of a system and its environment can be more enlightening with chaos theory as the tool, especially when explicating an historical personage or situation. Here the human being or set of human beings creates a pattern in the time-space, this pattern is the basin of attraction within which the attractor or multiple attractors form. The Newtonian paradigm of linear mechanics does not reveal all the ramifications that effect the event or person.