Chaos describes how a system’s dynamics over time may be sensitive to initial conditions, resulting in the potential for widely divergent outcomes given only very small differences in the system’s input values, thus making the future state of the system very difficult to predict. This chaotic and unpredictable behavior happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. A double pendulum is a classic example of a chaotic system, consisting of only two interacting components, each limb, with these limbs being both strictly deterministic when taken in isolation, but when we join them this very simple system can and does exhibit unpredictable chaotic behavior; starting the pendulum from a slightly different initial condition would result in a completely different trajectory.
