Chaos refers to the apparent randomness and unpredictability observed in certain nonlinear dynamical systems, despite being governed by deterministic laws. In mathematics, chaos often emerges in iterative processes where small changes in initial conditions can lead to vastly different outcomes.
Newton's Method: An iterative numerical method used for finding approximations to the roots (or zeroes) of a real-valued function.
Deterministic System: A system in which no randomness is involved in the development of future states; all future states are determined by the current state and its governing equations.
Sensitivity to Initial Conditions: \text{A property of chaotic systems where small changes in starting points lead} \text{to vastly different outcomes over time.}