An Introduction to Dynamical Systems and Chaos. Chaos theory. A double rod pendulum animation showing chaotic behavior.
Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. Chaos: When the present determines the future, but the approximate present does not approximately determine the future. Chaos. "Chaos" is a tricky thing to define.
In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. Gleick (1988, p. 306) notes that "No one [of the chaos scientists he interviewed] could quite agree on [a definition of] the word itself," and so instead gives descriptions from a number of practitioners in the field. For example, he quotes Philip Holmes (apparently defining "chaotic") as, "The complicated aperiodic attracting orbits of certain, usually low-dimensional dynamical systems. " What is Chaos? An Interactive Online Course for Everyone.