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No, by stirring you're just making the pile to move, and things descend down the gradient of gravity. :).

The little things moreso. Brazil nut effect!

When you stir, you're stirring in a pattern, probably a circular one. Plus you're probably not paying too much attention to the shape of the pile, so it's gradient-free. It's pattern search. Except it's only approximately a circular pattern. There are random variations. Stochastic pattern search.

So more like a genetic algorithm then?

GAs also exploit structure in the search space.

To see this most clearly, read up on estimation of distribution algorithms (EDAs), which generalise the ways in which GAs work.