Tree Fight!

Come on, you know it's a good idea.

Here's how I think it would work:
Players take turns placing new branch segments. They can make a branch taller by extending it, or they can split the branch by adding a joint. Sunlight comes down from the sky, nutrients come up from the earth (I suppose roots should be able to be grown, too), and you also need to have a water source (lack of any of these causes your tree to shrink or die).

Fighting involves blocking the other trees from vital resources by outmaneuvering them in growth. Every certain-number-of-turns, you are allowed to pick a survival adaptation (which you have earned from your years in the wild). These survival adaptations might allow you to store water more efficiently, fend off annoying animals, grow your roots deeper or your branches higher, or even live longer. Some adaptations would be fantastic, like the ability to grow explosive-fruit-launching branches and attack your rivals directly. Some would be taken from nature, like the ability to grow runners underground (and then start a new trunk elsewhere on the battlefield).

Each turn might also bring with it random events or hazards- animals, disease, forest fires, lumberjacks, or even a guerrilla war causing collateral damage. These are obstacles to avoid or even plan your strategy around (some plants thrive and spread with fires, for example).

Winning could be as simple as lasting a certain number of turns, or as complex and fantastical as evolving sentience or growing into space.

COME ON

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You could have the background flow up, so you could break through the clouds and eventually the atmosphere (after picking the appropriate adaptations), and then evolve little space-marine pods that you could send out against other space trees!

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And you could have the camera scale, so that you could see your whole tree at once (which would be really cool if, for example, your tree could grow from one planet to the next). You could conquer whole worlds! Maybe each world could be a new level, which you would have to conquer (remove all competition from), with space growing sequences in between. It could all just be one map! We could do this with simple, reusable graphics (unlike Necropopolis).