This is quite challenging! I was able to get to the 5th stage but somehow, I can't see the solution.
I'm a sucker for those kind of games, congrats, so far the demo is very attractive ;) The design is really charming despite its simplicity.
Gameplay-wise, the fact that once you grow, you can't go back makes every move important and I love that. Good thing we have an undo button. I know it's just a demo, but in the final game, I'd suggest to have a slower difficulty curve for the first few levels to ease the player in and make sure he understand everything he can do. For instance, I wasn't sure how properly to grow in different shape and already in the 3rd level, there was a big puzzle about it. Food for thoughts!
Otherwise, it's a very cool game. I'll try to beat it soon!
Congrats on a very interesting concept and I'll follow the development on Twitter for the full release!