THE RULES OF ATRAXI*

And now we turn our attention to the Atraxi, another alien race introduced in the season premiere of 'Doctor Who', "The Eleventh Hour". Unlike the Judoon, the Atraxi were not an inter-galactic police force, but instead inter-galactic prison guards.
These warders must have formed a symbiotic relationship with their spaceships, which could be related to the Crystalline Entity seen in 'Star Trek: The Next Generation'.
The Atraxi may not have actually been giant eyeballs. It could have been that they assumed that shape to impress upon their prisoners that the were always under a watchful eye.

The Atraxi were more than just an eyeball - they could speak, project astral images, and they could reason, which implies a brain and mind.

There's no way of knowing what the Atraxi are like as children, at least not from this 'Doctor Who' episode. But it could be that before they bonded with their own crystalline entities, each Atraxi had legs to get them about. And like other creatures, the Atraxi evolved - losing those limbs once they reached maturity and were bonded with their spaceships. Thanks to Bernard Cribbins' portrayal of Bilbo Baggins in an episode of 'Jackanory', we can claim now that "The Lord Of The Rings" is part of Earth Prime-Time. So it's pozz'ble, just pozz'ble as Mushrat would say, that the Great Eye of Sauron was a rogue Atraxi who turned to the Dark Side in its quest to conquer Middle Earth Prime-Time. BCnU!

*It's just a play on words. This is merely a Toobworld theory and is not meant to be taken as being anything near what Steven Moffat intended. I doubt that the Grand Moff and I would see eye to eye on this.

Sorry about that, Chief......