Breeding a lot of cows or spawning a lot of cows using mob eggs eventually causes the game to crash

What I expected to happen was to end up with a large amount of cows. Things didn't work out that way.

After a while trying to breed the cows the game crashed. I then restarted MC and resumed breeding, it then crashed again. The next day I created a new superflat world and started spawning them using mob eggs. I noticed the cows moved in a sluggish way, after which the game crashed again.

Steps to Reproduce:
1. Make a world
2. Spawn a lot of cows either by breeding or spawning them using mob eggs
3. Wait a long while
4. See the crash reports