The relevant features of both simple and completely random images can readily be recognized even at quite high levels of compression.

But if the sequence is random then what one hears is just an amorphous hiss.

And in fact, all that is really necessary is that the hashing procedure generate enough randomness that even though there may be regularities in the original data, the hash codes that are produced still end up being distributed roughly uniformly across all possibilities.

In particular, it might be thought that the behavior of systems like rule 30—while obviously at least somewhat computationally sophisticated—might somehow be too random to be harnessed to allow complete universality.

sorts of practical processes in which bias or deadlock can be avoided by using randomness, or in which one wants to generate behavior that is somehow too complex for an adversary to predict.

Even though it is not inevitable from lattice symmetry, one might think that if there is some kind of effective randomness in the underlying rules then sufficiently large patterns would still often show some sort of average isotropy. And at least in the case of ordinary random walks, they do, so that for example, the ratio averaged over all possible walks of n = 4 tensor components after t steps on a square lattice is β = 3 + 2/(t - 1) , converging to the isotropic value 3, and the ratio of n = 6 components is 5 - 4/(t - 1) + 32/(3t - 4) .

But if one assumes sufficient randomness in microscopic molecular processes they can also be derived from molecular dynamics, as done in the early 1900s, as well as from cellular automata of the kind shown on page 378 , as I did in 1985 (see below ). … For in particular it ends up being almost impossible to distinguish whatever genuine instability and apparent randomness may be implied by the Navier–Stokes equations from artifacts that get introduced through the discretization procedure used in solving the equations on a computer.

And as a first example, the picture on the facing page shows a rule that produces a pattern whose surface has seemingly random irregularities, at least on a small scale.

And indeed we know that this computation is useful in practice for generating sequences that appear random.

Most common is to assume that within each phoneme-length chunk of a few tens of milliseconds the vocal tract acts like a linear filter excited either by pure tones or randomness.