What is the technology used in iOS 11 settings migration (moving blue dots / particles pattern / animated QR code?)
The technology can be thought of very much like an animated QR-code. The main principle of data encoding is very much like QR-codes, but obviously with the difference that as time goes forward, the displayed data changes as an animation.

In addition there seems to be the use of a neat trick with two different colors shown in quick alternation, which makes it possible for Apple to "hide" or make less obvious the clues that are used for the receiver of the data to synchronize with the signal (i.e. figure out where the boundaries of the encoded data is).

With a traditional QR code these sync markers are much more evident as they are big black square boxes with white borders that are set different places in the code to make it easy for the receiver to figure out what's encoded data, and what's not part of the code.

Much more details are available in these two patent applications by Apple:

US Patent 9,022,291
US Patent 9,022,292