According to this article on c|net:
Two … users have now revealed functioning hard drives built inside Minecraft that can read and write data. The first, created by Reddit and Imgur user smellystring can store 1KB [sic] of data, while a second, larger unit created by The0JJ can store 4KB [sic] of data.
"One day we will build a full computer in Minecraft, then play Minecraft on it. then the universe will crash," writes Imgur user mkat10z. Turns out, someone has already done that, creating a 2D platformer version of Minecraft that you play within Minecraft on a redstone computer.
UPDATE: It appears the referenced article was in error; the actual capacities should be in kilobits.
(Score: 2, Informative) by Valkor on Friday August 22 2014, @06:34AM
Nope, they both exist. https://www.google.com/search?q=minecraft+in+minecraft [google.com]
(Score: 3, Informative) by maxwell demon on Friday August 22 2014, @07:00AM
I also found this. [youtube.com] So apparently also a computer in Minecraft has already been done.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by maxwell demon on Friday August 22 2014, @07:06AM
Further browsing reveald that also Conway's Game of Life has been implemented in Minecraft. Since the game of life is [youtube.com]turing complete, so is Minecraft, obviously. [rendell-attic.org]
The Tao of math: The numbers you can count are not the real numbers.