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Other uniformly distributed sequences Cases in which Mod[a[n], 1] is uniformly distributed include √ n , n Log[n] , Log[Fibonacci[n]] , Log[n!]
Distributed computing Many of the basic issues about the progress of time in a universe consisting of many separate elements have analogs in the progress of computations that are distributed across many separate computing elements. … But more theoretical investigations of formal concurrent systems, temporal logics, dataflow systems, Petri nets and so on have led to ideas about distributed computing that are somewhat closer to the ones I discuss here for the universe.
If the output from the generator was perfectly random, then in each case these points would be uniformly distributed.
The cellular automaton itself uses in effect a distributed representation of the density.
A typical kind of failure, illustrated in the pictures on the next page , is that points with coordinates determined by successive numbers from the generator turn out to be distributed in an embarrassingly regular way.
As mentioned on page 891 , having GoldenRatio turns between elements makes them in a sense as evenly distributed as possible, given that they are added sequentially.
Mechanisms that generally seem able to give α ≃ 1 include random walks with exponential waiting times, power-law distributions of step sizes (Lévy flights), or white noise variations of parameters, as well as random processes with exponentially distributed relaxation times (as from Boltzmann factors for uniformly distributed barrier heights), fractional integration of white noise, intermittency at transitions to chaos, and random substitution systems.
And the basic mechanism is typically some kind of progressive annihilation of elements that are initially distributed randomly.
Rate equations In standard chemical kinetics one assumes that molecules are uniformly distributed in space, so that the rates for particular reactions are proportional to the products of the densities of the molecules that react in them.
General powers [of numbers] It has been known in principle since the 1930s that Mod[h n , 1] is uniformly distributed in the range 0 to 1 for almost all values of h .