The Lorenz System

The Lorenz System is a set of three mathematical equations that model how certain complex systems, like weather patterns, evolve over time. It demonstrates how small changes in initial conditions can lead to vastly different outcomes—a phenomenon known as chaos. These equations describe variables related to fluid flow and temperature, creating intricate, unpredictable patterns called attractors. Despite seeming randomness, the system follows specific rules, illustrating how deterministic processes can produce unpredictable behavior, highlighting the sensitive dependence on initial conditions that makes long-term prediction challenging in complex systems like the atmosphere.