Apple wont boot after updating on Yosemite

After accepting a Yosemite update, my macbook won't boot. I already had Yosemite installed, but simply installed a systemupdate it has been asking for, for some time now.

When I boot up the computer, I see it loading (the usual loading screen, with the apple icon), but after a short while it stops with this screen:

I have tried resetting the SMC, and also tryed booting up in "Recovery mode", then running "Disk repair" from the disk utility. None of that has worked.