Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnectedness, 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 scientific theory and branch of mathematics focused on underlying patterns and deterministic laws, of dynamical systems, that are highly sensitive to initial conditions, that 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. An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior.
