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How Do Simple Programs Behave?…The Crucial Experiment How Do Simple Programs Behave? … How do such programs typically behave? … But with a computer it is straightforward to start doing experiments to investigate it.
What Perception and Analysis Do…What Perception and Analysis Do In everyday life we are continually bombarded by huge amounts of data, in the form of images, sounds, and so on. … And this is what perception and analysis attempt to do.
What Perception and Analysis Do…So how easy is it to do this? … For I suspect that there are fundamental limitations on what perception and analysis can ever be expected to do.
How Do Simple Programs Behave?…But where does this complexity come from? … But it turns out that even the most sophisticated mathematical and statistical methods of analysis seem to do no better.
How Do Simple Programs Behave?…And so the picture below shows what one cellular automaton does over the course of ten steps.
How Do Simple Programs Behave?…And as a result it becomes almost impossible to predict—even approximately—what the cellular automaton will do.
What Perception and Analysis Do
What Perception and Analysis Do
Note (f) for How Do Simple Programs Behave?…Note that GCD[m, n] yields a more complicated pattern (see page 613 ), as do JacobiSymbol[m, 2n - 1] (see page 1081 ) and various combinations of functions (see page 747 ).
How Do Simple Programs Behave?
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