Scene #1 contains moving layers, and layers that fade in and out, as well as a stationary layer in the far background to create depth.
Scene #2 is with the same concept as #1, except with the trees warped slightly to give depth. The samurai was created in a separate file to have the static effect, and then he was imported into the file.
Scene #3 is essentially a copy of scene #1, except the man is perceived to not be moving; and the camera is moving around him.
Some images from alternative source.
Background art by me.