Thrive

From the publisher:

Thrive is a two-player abstract strategy game with incredibly simple rules that grows in complexity as you play.You play as one of two lotus flowers, competing to control the pond. Be the first to capture all but one of your opponent’s seed pods and win this game of tactical decision making!

Each turn you move a piece, then add two additional pegs to any of your pieces, giving them more possibilities for movement on future turns.