SeedRandom[n] resets the pseudorandom number generator, using the integer n as a seed.
SeedRandom[ ] resets the generator, using as a seed the time of day.
You can use SeedRandom[n] to make sure you get the same sequence of pseudorandom numbers on different occasions.
You can also use SeedRandom["string"], although the seed set in this way may be different on different computer systems.
See The Mathematica Book: Section 3.2.3.
See also: Random, $RandomState.
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