I'm just speechless about that computed re-creation assembling the four frames. Brilliant.
The interpretation of the blank spot is also quite nice and very Escher-esque, with the content literally jumping out of the frame. Probably Escher left the center patch blank because his construction method would have him exceed some technical/physical limitation, so instead of drawing an approximation he preferred a void.
There's an OS X screensaver based on this work which animates the effect, in a similar way to "dive" animations into fractal images. Fascinating but also nauseating after a while.
(For the record, I do understand this article explores a different mathematical aspect of Escher than Hofstadter)