All you need to do is run a "dumb"[1] rsync to a backup provider running on ZFS, and the remote will have its own set of day/week/month snapshots - exactly like time machine[2].
Now if only there were such a provider ... standards based rsync over ssh ? Remote ZFS filesystem ? 12+ years of history providing that service ? Progressive stance on govt. monitoring ?[3] No, it would be too good to be true.
[1] Dumb, as in, just a straight 1:1 mirror.
[2] But independent - no relation to TM on your own system
One important difference between Time Machine and using rsync.net in the way you describe is that Time Machine doesn't require trusting anyone with your data[0].
Of course, it's possible to have encrypted snapshots on rsync.net with duplicity[1], the method I use. That being said, I have no particular reason to distrust rsync.net, and I have liked the service they have provided. If anything, I trust rsync.net more than other backup providers and certainly more than Apple.
[0]: Assuming Apple hasn't set up Time Machine to secretly send files back to Apple. But if you run Mac OS X, you're already trusting them not to do something like that.
Now if only there were such a provider ... standards based rsync over ssh ? Remote ZFS filesystem ? 12+ years of history providing that service ? Progressive stance on govt. monitoring ?[3] No, it would be too good to be true.
[1] Dumb, as in, just a straight 1:1 mirror.
[2] But independent - no relation to TM on your own system
[3] http://www.rsync.net/resources/notices/canary.txt