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I'm pondering over this research question.

Let's suppose you've got a bunch of units which can be colored black or white. They're roaming around 2d grid in random walk. Any time a unit meets with another unit, it has an option to change color. It doesn't have to though, depending on its internal logic. The point is to calculate how long will it take until all units over the grid are of the same color.

Anybody knows what this problem is called, and how to model it? Any advice would be appreciated.

I'm thinking of simple strategy like each unit counts the number of black and white units it met with, and as soon as one number exceeds the other, the unit will change color. Any ideas how to math model this?

Thanks,

Monte