Faraday waves are the ripples that form on a liquid surface when its container is shaken up and down; they are what most water cymatics actually shows. Laurette Tuckerman is a fluid dynamicist who has worked on the theory and simulation of these patterns for decades. This lecture, posted by the Israel Institute for Advanced Studies in 2017, covers the more unusual patterns, including the square, hexagonal and quasi-periodic arrangements that appear under certain driving conditions.
It is a talk for a physics audience, with equations, and it has a few thousand views rather than millions. We include it because it is the serious end of the subject: the same patterns the art videos show, treated as a problem in pattern formation with a real literature behind it.
If you want to know why a dish of water forms squares at one frequency and hexagons at another, this is where the answer lives.