Butterfly effect

Butterfly effect is a term coined by Edward Lorenz and illustrates the chaos system sensitive dependence on initial conditions. The Butterfly effect becomes famous due to the Lorenz's example of the initial condition sensitive phenomenon: "A butterfly flapping its wings in Brazil can set off a tornado in Texas".

In the following Java demonstration, the Butterfly effect is illustrated by showing the position across the iteration time, of two balls, which very (but not exactly equals) initial conditions on the Lorenz strange attractor (partial diferential equations bellow). Noticed the balls started its trajectories of almost the same point, but after a time, they can following completely different trajectories.

The Chaos Theory is a mathematics base for undertand complex phenomena in nature and can be used for a big amount of distinct applications. The SCG Group are interested in the following applications of the Chaos Theory: Pattern Recognition, Artificial Inteligence, Image Analysis, Cryptography, Information Theory, Random Numbers and Complex Systems Simulations.