The mushroom engine is based on Hempuli's "Jump on Mushrooms", so I shouldn't be credited for the idea in either case, I just did a new version because I loved Hempuli's game. The main difference between "The Mushroom Engine" and the original "Jump on Mushrooms" is that the time doesn't reverse before you reach the beginning of the first level, which was also something Hempuli requested me to change. By this reason, I only want to be credited as the programmer, Hempuli is the one with the ideas and the level design!
I have played Braid and love that game, Hempuli who have created the original Jump on Mushrooms haven't played Braid, but even if he actually had and got the entire idea from that I wouldn't see a problem with that. I totally like the idea about clones, demakes, and games heavily inspired by other games. In fact, no matter what you look at in my games, almost everything is taken from something else. The design of several rooms of the castle in Knytt is taken from Ico, the powerup pinpointer is from Shadow of The Colossus, the idea about patterns on surfaces in Knytt and KS is taken from Super Mario World, the ball material changing in WaDF and Night Game is inspired by Ballance, and Night Game is basically more or less a 2D take on Marble Madness with physics... The bonus song in Knytt (bouncy) is heavily inspired by "Nicotine" by Dr. Rockit, and a song underground near the castle in Knytt is inspired by one of the songs in the Samorost 2 soundtrack. The way I use ambiance sounds is something I learnt from Ico, and the way I use music in Knytt and Knytt Stories comes from Ballance. To be completely honest, I've never been that innovative.