Chaos theory is a branch of mathematics that studies how small changes in initial conditions can lead to vastly different outcomes. This concept is often illustrated by the famous butterfly effect, where the flap of a butterfly's wings in one part of the world could eventually cause a tornado in another. It shows that systems, like weather patterns or ecosystems, can be highly sensitive and unpredictable. In chaos theory, even seemingly random events can follow specific rules and patterns. This means that while we may not be able to predict exact outcomes, we can understand the underlying structures that govern chaotic systems. This has applications in various fields, including meteorology, economics, and even biology.