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Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0312) perturbations in the mirrors and by other phenomena that are not accounted for in the simple description we have given. At the heart of the system shown on the ...
Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0311) [No text on this page] Captions on this page: An arrangement of mirrors set up to exhibit randomness arising from sensitive dependence on initial conditions. The ...
Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0307) further. And then in the first case, the subsequent motion looks quite random. But in the second case it is fairly regular. So why is this? A little analysis ...
Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0309) being able to see a sequence of explicit bumps in the road, the initial conditions for the position of a point in the kneading process are encoded in a more ...
Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0314) the past taken as one of the key pieces of evidence for the idea that simple laws of nature could exist. But calculations imply that sensitive dependence on ...
Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0304) perfect randomness. And the reason for this is that there are almost inevitably correlations even in the supposedly random environment. In an ocean for example, ...
Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0306) The point then is that a human rolling the ball will typically not be able to control this speed with sufficient accuracy to determine whether black or white will ...
Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0313) exactly the same phenomenon of successively sampling less and less significant digits still occurs. And once again, at least for a while, any randomness in the ...
Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0305) the bumps, and if there is randomness in these bumps it leads to corresponding randomness in the motion of the car. A somewhat similar example is a ball rolled ...
Chaos Theory and Randomness from ...   (Stephen Wolfram's "A New Kind of Science")
(Page 0308) doubled. And when the material is cut and stacked, the effect on the number is then to extract its fractional part. But it turns out that this process is exactly ...
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