Perfect Shuffles of Playing Cards

Posted by Cleve Moler,

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When a deck of playing cards is shuffled perfectly, the result is not random. A perfect shuffle places the cards in a mathematically precise order. As a result, when the most common version of a perfect shuffle is repeated eight times, the deck returns to its original state.... read more >>

Fractal Global Behavior of Newton’s Method

Posted by Cleve Moler,

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When the starting point of Newton's method is not close to a zero of the function, the global behavior can appear to be unpredictable. Contour plots of iteration counts to convergence from a region of starting points in the complex plane generate thought-provoking fractal images. Our examples employ the subject of two recent posts, the historic cubic $x^3-2x-5$.... read more >>

Charles Lawson, 1931 – 2015

Posted by Cleve Moler,

Chuck Lawson passed away in July at the age of 83. Chuck was one of the people who introduced me to computing and mathematical software. I worked for him at Caltech's Jet Propulsion Laboratory during the summers of 1961 and 1962, just before and after my first year in grad school.... read more >>

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