For most of these networks there is no way of laying out their nodes so as to get a picture that looks like anything much more than a random jumble of wires.

A cellular automaton set up to emulate random-access memory in a computer.

Uniformity in frequency As shown on page 587 , a completely random sequence of cells yields a spectrum that is essentially uniform in frequency.

If the connections in a network are chosen at random—as in case (j)—then again there will almost never be the kind of locality that is needed to get something that corresponds to ordinary finite-dimensional space. … And so at the level of individual connections, the network will most likely at first look quite random.

First, that typical images of relevance tend to be far from random—indeed they often involve quite limited numbers of distinct objects.

Some 2D Turing machines exhibit elements of randomness at some steps, but then fill in every so often to form simple repetitive patterns.

And in such cases, the packing of atoms is quite random—except that locally there is often approximate icosahedral structure, analogous to that discussed on page 943 .

At the atomic level, a simple model suggested fairly recently is that atoms are connected by bonds with a random distribution of strengths, and that cracks follow paths that minimize the total strength of bonds to be broken. … In recent years, computer simulations with millions of atoms have been carried out—usually with realistic but complicated interatomic force laws—and some randomness has been observed, but its origins have not been isolated.

Randomness in markets After the somewhat tricky process of correcting for overall trends, empirical price data from a wide range of markets seem to a first approximation to follow random walks and thus to exhibit Gaussian fluctuations, as noted by Louis Bachelier in 1900.

Iterative improvement [of constraint satisfaction] The borders of the regions of black and white in the picture shown here essentially follow random walks and annihilate in pairs so that their number decreases with time like 1/ √ t .