Issues with seeding a pseudo-random number generator more than once?

Question

I\'ve seen quite a few recommendations for not seeding pseudo-random number generators more than once per execution, but never accompanied by a thorough explanation. Of cour

Answer 1

Each time you call a pseudo-random number generator function, the generator takes some internal state and produces a pseudo-random number and a new internal state. The algorithm for transforming the internal state is carefully chosen so the output appears random.

When you seed the random number generator, you're basically setting this internal state. If you reset the internal state to some predictable value, you'll lose the appearance of randomness.

For example, a popular, simple RNG is a linear congruential generator. Numbers are generated like this:

X[n+1] = (a X[n] + c) mod m

In this case, X[n+1] is both the result and the new internal state. If you seed the generator every time as you suggest above, you'll get a sequence that looks like this:

{(ab + c) mod m, (a(b+1) + c) mod m, (a(b+2) + c) mod m, ...}

where b is your seed_base. This doesn't look random at all.