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Order out of noise — page 2

Random processes that reliably produce the same shape, and the reason that is less mysterious than it looks.
Where a long orbit of the logistic map spends its time. A histogram of 60000 iterates in 32 bins, with the density the map preserves drawn over it as the exact share each bin should hold. Dynamics

The histogram an orbit leaves

When no single step of an orbit is worth reporting, what is left is where it spends its time. That distribution is not uniform, it does not depend on where the orbit started, and it can be computed in closed form.

 Sampling the orders, and how fast the answer arrives. The largest error in the estimated shares against the number of orderings sampled, both on logarithmic axes, with the square-root rate drawn through the first point. Applied

Too many orders to list

The rule is an average over every order the players could have arrived in. At seven players that is five thousand orders and at twenty it is more than there are seconds in the age of the universe — so the average is sampled, and the error falls at a rate that can be measured.

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