This was very odd - the other day, I noticed some poop floating down from my betta, and suddenly he started swimming after it like it was some food! He did manage to get it into his mouth,
but he promptly spit it out. The next time I saw him looking at his own poop, I tried to use my finger on the outside(which he likes to follow) to steer him away until it hit the bottom. This was very odd to me, and I was wondering if anyone else's betta ever does this?! 
