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Note (e) for The Intrinsic Generation of RandomnessRandomness in Mathematica SeedRandom[n] is the function that sets up the initial conditions for the cellular automaton. The idea of using this kind of system in general and this system in particular as a source of randomness was described in my 1987 U.S. patent number 4,691,291.
For one might have assumed that any apparent randomness in the final shape of something like a crystal must always be a consequence of randomness in its original seed, or in the environment in which it grew. But in fact, as the pictures below show—and as we have seen many times in this book—it is also possible for randomness to arise intrinsically just through the application of simple underlying rules. And contrary to what has always been assumed, I suspect that this is actually how the apparent randomness that one sometimes sees in shapes formed by crystalline materials often comes about.
Note (b) for Randomness from the Environment…Randomness in computer systems Most randomness needed in practical computer systems is generated purely by programs, as discussed on page 317 . But to avoid having a particular program give exactly the same random sequence every time it is run, one usually starts from a seed chosen on the basis of some random feature of the environment. Until the early 1990s this seed was most often taken from the exact time of day indicated by the computer's clock at the moment when it was requested.
There are 32 possible symmetric such rules with just 4 immediate neighbors—of which 16 lead to growth (from any seed), and all seem to yield at least approximately circular clusters (of varying densities). … Note that even though the underlying rule involves randomness definite geometrical shapes can be produced. … But most generalized aggregation models do not have this property: instead, the form of their internal patterns depends on the sequence of random choices made.