From the beginning, the link between LFSRs and PEAC was clear, if only the right perspective was used.

So I made an emulation with CircuitJS to make it obvious:

The w4 configuration has a pair of orbits with 135 steps, which don't fit in the screen.

Each level is made of 2 DFF and one full-adder, just like a 2-tap Fibonacci LFSR with a more complex feedback circuit:

One possible application is as a serial-line scrambling circuit (think Ethernet, USB and other asynchronous links), since it can't "get stuck" like a LFSR.