The new science called ‘chaos theory’ has caught the popular imagination. Newton’s clockwork was jolted when quantum mechanics revolutionized the world of the small. Then, for the everyday world of dripping taps, chaos swept in to solve longstanding anomalies. It shows how a universe of deterministic laws is predisposed to disorder and complexity, with the ‘butterfly effect’ giving an insuperable sensitivity to initial states. Beautiful graphics, which make the subject so appealing, are here used to explain the unpredictability. Simple equations fed into a computer produce breath-taking fractals of ever-increasing complexity. Cutting across traditional disciplines, chaos is used to control lasers, improve weather forecasting and devise fuel-efficient trajectories for space-craft. It is especially valuable in monitoring heart-beat abnormalities. Interactive talks and discussions, with over 100 colour images, dramatic experiments and videos, show chaos theory at work. Simple apps can be used at home.