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A while back when I was researching spawning rules, I found that if a monster in the 32m - 128m area (which randomly despawns over time), would actually not despawn if it was moving. So if the Mob was in a water channel and moving, then it wouldn't despawn if the player moved so that the mob was over 32m, as long as the mob didn't reach 128m+.

Is this still true in the newest 1.8 version?

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All of the spawn rules can be found Here. In case the website is down, here's a useful excerpt:

Monsters (not holding items or wearing armor) and squid (but not animals), including hostile wolves as of 1.1, can cease to exist, or "despawn", under certain conditions:

A mob that has had no player within 32 blocks of it for more than 30 seconds has a 1 in 800 chance of despawning on each game tick (1/20th of a second). Therefore, the half-life of monsters not within 32 blocks of a player is 27.73 seconds (after the initial 30 seconds have elapsed).

A mob will immediately despawn if there is no player within 128 blocks of it. Note that this is a Euclidean sphere, not a cylinder from map top to bottom and not a taxicab sphere (which is more like an octahedron). Example: A mob at 0/y/0 will remain at least 30 seconds (as above) if the player moves to 65/y/65 (real distance 91.9), but despawns immediately if the player moves to 91/y/91 (real distance 128.7).

All hostile mobs (including those that are holding items) in a world will despawn if the difficulty is set to peaceful, regardless as to where the player is positioned in the world.

In multiplayer, despawning does not occur while there are no players in the game.

A monster which has been named with a name tag will not despawn. However, one created from a renamed spawn egg will despawn as normal.

If a monster is holding any items or wearing any armor that was given by a player or picked up from the ground, it will not despawn.

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    This doesn't seem to have answered the OP's question - he specifically asked about whether mobs despawn when more than 32 and less than 128 blocks away, if they are moving.
    – Johonn
    Sep 18 '14 at 23:18
  • "These are all the rules"... and the OP's hypothetical rule is not part of them. I think that makes it an answer. (The OP probably didn't realise that there's an average 1 minute delay between moving 32m away and mobs despawning, and erroneously attributed the effect to the movement.) Mar 4 '15 at 3:15

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