The Lorenz Attractor

The Lorenz Attractor is a mathematical model that describes chaos in fluid flow, originating from weather prediction studies. It uses three equations to represent how certain systems evolve over time, producing complex, unpredictable patterns. Despite appearing random, these patterns are deterministic, meaning they follow specific rules. The attractor forms a shape resembling a butterfly or figure-eight, illustrating how tiny differences in initial conditions can lead to vastly different outcomes—a concept known as sensitive dependence on initial conditions or chaos. It exemplifies how complex systems can have underlying order even when their behavior seems unpredictable.