This mod will make trees automatically reproduce and expand over time.
The growth rate is very low (otherwise you'd drown in forest in long game),
but you can configure it in config.lua if you want.

Other things being worth noting are:

• There's a hard limit on tree count, whose default value is 800000, so
  your save file won't get super-heavy.

• Trees won't grow on sand, stone path or concrete, so pave your base to prevent
  them from entering.

• Trees too far from any of player's entities (about 192 tiles) won't grow,
  because it would make the game and save file unnecessarily heavy.

• Debug mode shows count of existing trees and trees which have been added.

• Multiplayer is not tested. This mod uses Lua's math.random(), which could
  cause problems on multiplayer game and replays.

• Although this mod gradually processes all trees in the game, the algorithm is
  highly optimized so that execution time per tick is very low.
  You won't feel a 'micro freeze' unless the game is very big.

Now get your flamethrower ready!