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Scrambled Grids

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Author:Ivars Peterson (MathTrek)
Description: The so-called baker's map, or transformation, in dynamical systems theory. One special case: Start with a square. Stretch it to twice its original length while making it half as wide. Cut the result in half, and stack one half on top of the other to return the combination to the square's original dimensions. The square's area is preserved, but its components are rearranged. During the mixing process, some of the square's points occasionally come back close to their initial locations within the square. This is known as Poincaré recurrence: if a transformation is applied repeatedly to a mathematical system and the system cannot leave a bounded region, it must return infinitely often to states near its original state.... Bob Brill's interest in algorithmic art using grid-scrambling transformations is illustrated.

Levels: High School (9-12), College
Languages: English
Resource Types: Articles
Math Topics: Prime Numbers, Algorithms, Transformational Geometry, Art

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