- Complete disorder and confusion.
- A Lorenzian water wheel, which is a Ferris wheel-type contraption with equally spaced buckets of water that rotate around in a circle. Now imagine water being dripped into the system at the very top. Each bucket has a leak, so some water escapes into whatever bucket is directly below the drip. Depending on the rate of the water coming in, this system exhibits a chaotic process that depends on molecular-level interactions of water molecules on the sides of the buckets. Read more about it in this associated Wikipedia article.
- In mathematics we have chaos theory focused on the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect.
- Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.
- This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved.
- Chaotic behavior exists in many natural systems, such as weather and climate. It also occurs spontaneously in some systems with artificial components, such as road traffic.
- Chaos theory has applications in several disciplines, including meteorology, sociology, physics, environmental science, computer science, engineering, economics, biology, ecology, and philosophy.