A remarkably unfinished tiling window manager work-in-progress extension for gnome-shell.
To run it in gnome-shell, you will have to compile and run my mutter fork. I'm afraid I can't help you with how to do that, as the gnome build system is big and complicated, and you're probably better off just waiting until my patches are accepted (or I figure out something better).
To run in gnome-shell, you should be able to clone this repo (or make a symlink) in
/firstname.lastname@example.org/. Depending on your version of gnome-shell, you'll need to modify metadata.json as the shell will refuse to load extensions for a different version of gnome-shell.
Keyboard shortcuts are all manner of broken. I have tried to emulate bluetile's shortcuts for the most part, except that almost all win+[letter] keyboard shortcuts do not work in gnome-shell. So for now you have to use win+alt+[letter]. Oh, and you have to press alt before you start pressing the windows key, because that's apparently a thing.
To try out all the tiling behaviour in a web browser (not very useful, but a whole lot easier than installing right now), you can peek at the jQuery mockup
This extension is best used with the natural window placement extension. I personally recommend the alternate status menu extension as well, because not providing a power-off menu item is ridiculous.