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Deterministic random number generators (RNG) are designed to provide faithful approximations of a uniform distribution.

Given that a deterministic RNG always gives the same sequence for a given initial state (e.g. a seed), my question is: can we represent them as a (chaotic) dynamical system?

If so, how the properties of the RNG (e.g. "faithfulness") relate with the properties of the dynamical system such as the Largest Lyapunov exponent (largest LE)?

For instance, I suspect that a large Lyapunov exponent is good from the RNG point of view since more entropy is produced, but it seems to me that it is not enough to have a large Lyapunov exponent.

I found this work where the authors make such claim, but they don't provide any insight about the RNG properties.

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You can, but the question is, what does it buy you?

I'd say the goal of chaos theory is to describe the behaviour of systems which look random at the first glance, yet do show some amounts of order, like attractors.

The goal of a RNG, however, is to produce a system which looks purely random no matter how hard you try to find some resemblence of order.

In other words, whenever a result about chaotic systems applies to your RNG, chances are that the RNG isn't very good...

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  • $\begingroup$ Buys me understanding about something that I don't understand - RNGs - from the perspective of something that I grasp (chaos theory). $\endgroup$ – Jorge Leitao Dec 9 '13 at 14:06

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