## Chaos theory |

**Chaos theory** is a branch of ^{[1]}^{[2]} Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of ^{[3]} The ^{[4]} A metaphor for this behavior is that a butterfly flapping its wings in China can cause a hurricane in Texas.^{[5]}

Small differences in initial conditions, such as those due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.^{[6]}^{[7]} This can happen even though these systems are ^{[8]} and is fully determined by their initial conditions, with no ^{[9]} In other words, the deterministic nature of these systems does not make them predictable.^{[10]}^{[11]} This behavior is known as **deterministic chaos**, or simply **chaos**. The theory was summarized by ^{[12]}

Chaos: When the present determines the future, but the approximate present does not approximately determine the future.

Chaotic behavior exists in many natural systems, including fluid flow, heartbeat irregularities, ^{[13]}^{[14]}^{[8]} It also occurs spontaneously in some systems with artificial components, such as the ^{[15]}^{[3]} This behavior can be studied through the analysis of a chaotic ^{[8]} ^{[16]} ^{[17]}

- introduction
- chaotic dynamics
- spontaneous order
- history
- applications
- see also
- references
- further reading
- external links

Chaos theory concerns deterministic systems whose behavior can in principle be predicted. Chaotic systems are predictable for a while and then 'appear' to become random.^{[7]} The amount of time that the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the ^{[18]} In chaotic systems, the uncertainty in a forecast increases ^{[19]}