Chaos is the apparently random behavior of systems that are governed by simple equations and rules. Such systems have the property that a tiny change in their starting condition drastically alters their future behavior, just as a butterfly flapping its wings in Brazil can cause a tornado in Texas a few weeks later. These computer simulations show many examples of mathematical systems that exhibit chaos, and you can adjust the parameters of the equations and explore their effect. You will note that many of the examples produce beautiful geometric patterns that are called "fractals," often considered the "fingerprints of chaos."