[Doctor Stochastic]

There are some old (half century or more) models of self-reproducing machines that work just like described. There's a bag of parts; if no parts are assembled, the shaking does nothing. If two (or more) parts happen to latch on to each other, the whole bag becomes full of that configuration.

[PatrickHenry]

If two (or more) parts happen to latch on to each other, the whole bag becomes full of that configuration.

And in organic chemistry, they can't help doing so. The oceans quickly fill with sub-assemblies of organic molecules.