# Chaos

Chaos

Chaoticians have learned to expect
That each butterfly has an effect.
Is its flapping a crime
Against order and time?
All the oracles’ futures are wrecked!
Mike Scholtes, Butterfly Effect

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## Introduction1

### Dictionary

chaos : the inherent unpredictability in the behavior of a complex natural system — Merriam-Webster   See also OneLook

### Encyclopedia

Chaos may refer to any state of confusion or disorder. — Wikipedia

Chaos (Encyclopædia Britannica)

Chaos (CompLexicon, Exploratorium)

### Search

Chaos (WolframAlpha)

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## Foundation

### Theory

Chaos Theory is the field of study in mathematics that studies the behavior and condition 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 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. 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 several disciplines, including meteorology, sociology, physics, computer science, engineering, economics, biology, and philosophy. A traffic model was developed showing that the system dynamics can pass under certain conditions to chaos. — Wikipedia

Butterfly Effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

The term, coined by Edward Lorenz, is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that was rounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.

Though Lorenz gave a name to the phenomenon, the idea that small causes may have large effects in general and in weather specifically was earlier recognized by French mathematician and engineer Henri Poincaré and American mathematician and philosopher Norbert Wiener. Edward Lorenz’s work placed the concept of instability of the earth’s atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos. — Wikipedia

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## Innovation

### Science

James Gleick on Chaos: Making a New Science (Video Interview, Open Road Media)

### Technology

How Chaos Theory Works (HowStuffWorks)

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## Preservation

### History

When the Butterfly Effect Took Flight (Peter Dizikes, MIT Technology Review)

### Library

Subject: Chaos (Library Thing)

Subject: Chaos (Open Library)

Subject: Chaos (Library of Congress)

Subject: Chaos (WorldCat)

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## Participation

### Education

Chaos Theory (Learning Theories)

### Organization

Society for Chaos Theory

### News

Chaos: An Interdisciplinary Journal of Nonlinear Science (American Institute of Physics)

### Book

The Chaos Hypertextbook (Glenn Elert)

### Bibliography

Biological Chaos and Complex Dynamics (David A. Vasseur, Oxford Bibliographies)

### Government

Managing Chaos and Complexity in Government: A New Paradigm for Managing Change, Innovation, and Organizational Renewal (L. Douglas Kiel)

Chaos (USA.gov)

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## Expression

### Game

Wolfram’s Chaos Game (Wolfram MathWorld)

### Arts

What does Chaos Theory have to do with Art? (Dean Wilcox)

### Visual Arts

Gary Eyster – Chaos Theory and Art (Adam Free, The Engineering of Conscious Experience)

### Language Arts

Popular Chaos Theory In Literature Books (Goodreads)

### Poem

The flap of a butterfly’s wing
Causes chaos: that one little thing
Gave the markets a lift,
And made fractal bloke Mandelbrot king. — Rory Ewins, chaos theory

OEDILF: The Omnificent English Dictionary In Limerick Form

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