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But it turned out that this particular kind of system, set up as it was on a square grid, was almost uniquely unable to generate the kind of randomness that we have seen so often in this book, and that is needed to obtain standard large-scale fluid behavior.

Note (d) for Space as a Network

And similarly, one can for example look at the statistics of random walks on the network.

Note (b) for Intelligence in the Universe

When galactic radio emission was first noticed by Karl Jansky in 1931 it seemed too random to be of intelligent origin.

Note (c) for Origins of Simple Behavior

(The more usual version of the model adds to a random cell.)

Note (a) for Fluid Flow

There is overall periodicity much like in a vortex street, but the detailed motion of the fluid is increasingly random.

Note (b) for Irreversibility and the Second Law of Thermodynamics

In responding to objections concerning reversibility Boltzmann realized around 1876 that in a gas there are many more states that seem random than seem orderly.

Note (a) for Computational Irreducibility

Sometimes the idea was to use randomized methods to get a statistical approximation to properties say of spin systems or lattice gauge theories.

Note (b) for Why These Discoveries Were Not Made Before

Games are normally based on definite rules, but are set up so that at each step they involve choosing one of many possibilities, either by skill or randomness.

Note (d) for Why These Discoveries Were Not Made Before

What has survived mostly shows repetitive patterns, but the ice-ray style, probably going back to 100 AD, has approximate nesting, though with many random elements.

Note (b) for Why These Discoveries Were Not Made Before