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|Ivars Peterson (MathTrek)|
|Music, dance, and chaos... The image on the computer screen resembles a delicate, stylized butterfly with translucent wings held lazily askew. It's called the Lorenz attractor, named for meteorologist Edward N. Lorenz of MIT, who in 1963 discovered this curious form encoded in a set of equations describing air flows in the atmosphere. The computer image arises out of a chaotic - in the mathematical sense - system. For a given starting point, the computer calculates the coordinates of each successive point as the dynamical system described by the equations evolves... Different starting coordinates typically lead to radically different sequences of calculated points. The overall pattern, however, can always be identified as the Lorenz butterfly. It's an example of both the sensitive dependence on initial conditions and the distinctive patterns that are characteristic of chaotic systems...|
|Levels:||Middle School (6-8), High School (9-12), College|
|Math Topics:||Chaos, Music|
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