káoszelmélet

Káoszelmélet, also known as chaos theory, is a branch of mathematics and physics that studies the behavior of dynamical systems that are highly sensitive to initial conditions. This sensitivity is famously referred to as the "butterfly effect," where a small change in one state of a deterministic nonlinear system can result in large differences in a later state. Despite being deterministic, meaning their future behavior is fully determined by their initial conditions and governing equations, these systems exhibit behavior that appears random and unpredictable over time.

The theory emerged from the work of mathematicians and meteorologists like Henri Poincaré and later Edward Lorenz. Lorenz's discovery in the 1960s, while working on weather prediction, highlighted how minuscule rounding errors in his computer simulations could lead to drastically different weather forecasts. This underscored the inherent unpredictability of complex systems, even with perfect models.

Key concepts in chaos theory include attractors, which are the states to which a system tends to evolve over time, and fractals, which are geometric shapes that exhibit self-similarity at different scales. Chaos is not synonymous with randomness; rather, it describes a type of complex, unpredictable behavior within deterministic systems. The study of chaos theory has found applications in diverse fields, including meteorology, economics, biology, engineering, and even social sciences, providing insights into phenomena that were previously considered inexplicable.