Difference Procedural Generation and Random Generation

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procedural

Today, I got into an argument about the term "procedural generation".

My point was that its different from "classic" random generation in the way that procedural is based on a more mathematical, fractal based, algorithm leading to a more "realistic" distribution and the usual randomness of most languages are based on a pseudo-random-number generator, leading to an "unrealistic", in a way, ugly, distribution. This discussion was made with a heightmap in mind.

The discussion left me somehow unconvinced about my own arguments though, so, is there more to it? Or am I the one who is, in fact, simply wrong?

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