![]() The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. ![]() The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.Ĭhaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. ![]() A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. ![]() For other uses, see Chaos theory (disambiguation). ![]()
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