Randomness, Chaos, and Fractals
In the previous lessons, we considered the extrapolation problems in which the result was, in principle, predictable, in the sense the more patterns we know, the better our predictions can be. In many practical problems, however, the analyzed process has a random component that is impossible to predict even if we have many patterns. For example, we may be able to predict how the Internet grows with time, but it is difficult to predict the delay of a single message sent through the Internet. In such situations, when we cannot determine the exact value, we may be able to determine the probabilities of different possible values. In this lesson, we show how continuous mathematics can help in in computing these probabilities, and how fractal theory can help to interpret the results in visual geometric form.
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