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This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Chaos_theory


00:00:30 1 Introduction
00:01:01 2 Chaotic dynamics
00:01:31 2.1 Chaos as a spontaneous breakdown of topological supersymmetry
00:02:02 2.2 Sensitivity to initial conditions
00:02:32 2.3 Non-periodicity
00:03:03 2.4 Topological mixing
00:03:34 2.5 Density of periodic orbits
00:04:04 2.6 Strange attractors
00:04:35 2.7 Minimum complexity of a chaotic system
00:05:36 2.8 Infinite dimensional maps
00:06:52 2.9 Jerk systems
00:07:53 3 Spontaneous order
00:08:24 4 History
00:09:25 5 Applications
00:09:56 5.1 Cryptography
00:10:26 5.2 Robotics
00:10:57 5.3 Biology
00:11:27 5.4 Other areas
00:12:13 6 See also



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SUMMARY
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Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Chaos theory is an interdisciplinary theory stating that within the apparent randomness of chaotic complex systems, there are underlying patterns, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state, meaning there is sensitive dependence on initial conditions. A metaphor for this behavior is that a butterfly flapping its wings in China can cause a hurricane in Texas.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. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as:
Chaos: When the present determines the future, but the approximate present does not approximately determine the future.

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. This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Chaos theory has applications in a variety of disciplines, including meteorology, anthropology, sociology, physics, environmental science, computer science, engineering, economics, biology, ecology, and philosophy. The theory formed the basis for such fields of study as complex dynamical systems, edge of chaos theory, and self-assembly processes.