Off-topic: Rhomboid beach patterns

I took a mini-break Sunday and went to the beach.

I noticed something I had never seen before, and it was driving me crazy. When the ocean waves retreated (backwash), they left consistent diamond-shaped patterns in the sand behind. The lines were never perpendicular to the shore, but rather perhaps at 80 degree and 100 degree angles facing the shoreline.

Here is the pattern being left behind on dry sand as the water (upper left) retreats:

Here is it while the sand is still wet from the backwash, contrast added to make it more obvious:

So I did a little Internet sleuthing. While I couldn't find many photos of similar patterns, apparently they are common. Here is an abstract from an article in the The Encyclopedia of Beaches and Coastal Environments:

Rhombohedral ripples are so common on the lower foreshore of a beach that Johnson (1919) called them backwash marks . The flow of the backwash down a beach often results in diamond-shaped rhombohedral ripples of low height that are best recognized by the criss-crossed pattern of intersecting lines of the lee slopes of the ripples. Generally there is a well-developed scour on the seaward side of the ripple rhombs, whereas the landward side of the diamond shape is more gentle.

Rhombohedral ripples seem to have been first described by Williamson (1887), who viewed them as resembling "the overlapping scale leaves of some cycadean stems." Observations by Woodford (1935) and Demarest (1947) show that rhomboid ripples form as a lee wave, radiating seaward from coarser than usual grains or more compact sand or from centers of escaping interstitial water. Rhomboid ripples form only in the water-saturated lower part of beaches that slope between 2 and 10 degrees (Emery, 1960). ...

I found a couple of other papers which went into math that is way beyond me. Also some claim that these patterns come from things like seashells sticking out of the sand, but the pattern was way too regular.

Apparently, there is no definitive answer as to why these patterns get generated, although there are some people who have worked very hard at figuring this out. (My initial guess was resonance patterns from the sound of the surf, but then the slope of the beach shouldn't matter.)