What happens when you bounce a ball on a table which is moving up and down? What if the ball has a hard side and a soft side? Analysis of the equations describing the motion of the ball and the table show that the resulting system can be chaotic, with very small changes to the initial conditions leading to quite different behaviour over time.
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Many real-world processes are chaotic: this is why weather forecasting is so difficult! Researchers at UNSW use mathematics and computer simulations to gain a better understanding of chaotic systems.