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Butterfly Effect

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"At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one and then several units in the last decimal place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution. " (E. N. Lorenz, The Essence of Chaos, U. Washington Press, Seattle (1993), page 134)

The Waiter Rule was first proposed by newspaper columnist David Barry in the late 1990s. It preposes that a person’s true character is revealed by […]The simplest mathematical framework exhibiting sensitive dependence on initial conditions is provided by a particular parametrization of the logistic map :In turn-of-the-century Vienna, a magician uses his abilities to secure the love of a woman far above his social standing.


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