> There's elegance and quite likely reduced computational load in a functional approach that can give the wave height value with only the inputs of the coordinates and time.

Sure, except there isn't any known closed-form expression that can model water waves in cases like the author is aiming for. (In the steady state water waves are roughly trochoidal, not sinusoidal, if you're interested.)

What happened in this article was that the author started with a mental image of what a water drop looks like, then hammered on a sin function until there was a resemblance. That's fine in and of itself, but he might as well have drawn a picture! Whatever resemblance he did or didn't achieve to actual water was a function of how good his mental image was and how long he spent working on the similarity, not a byproduct of the math involved.

What's nice about my awful stateful approach is that the physicality arises unbidden. If you code it up it will behave like water all on its own - you won't have to randomly fiddle with it like the article's author.

Also, with my version you don't have to start out knowing what water waves look like. It will show you. ;)