"Creating movies which don't exist" is the same as "creating movies".

Nice one, reminds me of L-Space in the Discworld books.

"Additionally, one can read any book ever written, any book that will be written at some point and books that were planned for writing that were not, as well as any book that could possibly be written." [0]

[0]: https://wiki.lspace.org/mediawiki/L-space

Infinite monkeys on infinite typewriters can produce a work of Shakespeare.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

Or infinite AI creating infinite movies can create Avatar.

I remember there being an archive that indexed a random stream of numbers from which you could download a range of random bytes, the idea being theoretically everything can be found within the dataset. I think it was done in protest of copyright or something like that.

I can't remember the name of it for the life of me.

Library of babel?

Yep - Vsauce has a nice video here: https://www.youtube.com/watch?v=k1bbInWfAgA

Do monkeys really produce an uniform distribution of keystrokes? Humans don't, and they're also primates.