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Windows 8, java 7 update 51
I was trying to create a machine that would take mobs and put them in minecarts when i noticed that some mobs moved their minecarts and others did not. This was weird, as mobs do not have pathfinding when riding in minecarts. For example, zombies riding minecarts do not react at all when close to villagers. Therefore it would make sense that mobs should not be able to control the minecart they are riding as they do not have pathfinding.
To investigate the cause of this bug I set up a system that places mobs in minecarts and tested it with creepers. Pictures 1 shows a creeper being placed in the mechanism. The minecart eventually comes to a stop (picture 2), showing that the creeper did not control the minecart at all. Placing cats next to the creeper (picture 3) also caused no response, which further shows that the creeper was not in control of the minecart.
For the second test, I placed a cat close to the rails and then summoned the creeper so that it would flee and thus BE IN MOTION when the minecart picks it up (picture 4). In picture 5 we see that the creeper goes forward in a similar matter to the first test. However, the creeper then stops and starts going backwards (picture 6), which is very weird.
We saw from the previous test that the cat should not affect the creeper when it is riding the minecart, and therefore there is no reason why test 1 and 2 should have different results. The only difference is that the creeper had momentum BEFORE it was picked up in test 2, whereas in test 1 it was stationary. My hypothesis is that when mobs enter minecarts, they keep whatever pathfinding they had before and try to get to the direction they were going before by controlling the minecart.
To conclude, mobs should not control minecarts, but test 2 shows that they sometimes can, and thus this bug should be fixed.
Here is a world download if you want to see the bug for yourself:
There is a cat spawn egg for your convenience.
Edit: I uploaded Picture 7 with the debug screen so you can see the version and a better view of the machine as well.