luismedel

The earliest jaw-dropping water effect I saw (and somewhat understood at 14) was the awesome credits scene from the Iguana's Earthquake demo[0].

The code[1] contains the following explanation (ancient DOS chars fixed with chatGPT)

  ; // UpdateTable : performs one integration step on U[CT]
  ; Differential equation is:  u  = a²( u  + u  )
  ;                             tt       xx   yy
  ;
  ; Where a² = tension * gravity / surface_density.
  ;
  ; Approximating second derivatives by central differences:
  ;
  ;  [ u(t+1)-2u(t)+u(t-1) ] / Δt² = a² (u(x+1)+u(x-1)+u(y+1)+u(y-1)-4u) / h²
  ;
  ; (where Δt = time step, h=Δx=Δy = mesh resolution)
  ;
  ; From where u(t+1) may be calculated as:
  ;                   ┌   1   ┐
  ; u(t+1) = a²Δt²/h² │ 1 0 1 │u - u(t-1) + (2-4a²Δt²/h²)u
  ;                   └   1   ┘
  ;
  ; When a²Δt²/h² = ½ last term vanishes, giving:
  ;                   ┌   1   ┐
  ;        u(t+1) = ½ │ 1 0 1 │u - u(t-1)
  ;                   └   1   ┘
  ;
  ; This needs only 4 ADD/SUB and one SAR operation per mesh point!

Maybe the OP's "not that important" was an unfortunate way to put it.

I think the answers you ask for are in Ordinatio Sacerdotalis[0]

FYI, you can download the source code [1].