How do forests grow in Alpha Centauri?

How many adjacent squares of forest do I have to plant before they will begin to expand?

And is there a formula, such that the more adjacent forest squares, the greater chance of auto expansion?

I don't have an authoritative answer, but I believe that each turn, each forest square has a very small chance of expanding to a random adjacent square. So the more forest squares already on the map, the more random forest square expansions will occur per turn. I believe this expansion mechanic also applies to fungus, but is less noticeable to the player since the game doesn't notify you of fungus expansions like it does for forest expansions.