Very nice and creative use of the game of life rules, being able to step back and forth felt good and the level design was solid.
I wonder how it would play if your moves were turn based as well instead of the platforming mechanics with more focus on puzzling mechanics and solutions like interacting with cells in different ways (like you have one insert/delete operation to do and you have to choose wisely etc). Or just with some form of undo as it-is to ease on the memorization/precision aspect a bit.
Think the level menu could automatically select the just unlocked level for you (or just go there automatically) for a more seamless experience. Having your progress saved here was a nice touch!
Overall a great entry with a high level of polish!