Here's something that seemingly defies explanation. Well, in point of fact, it does defy explanation. My explanation anyway.
Basically you're seeing a special type of standing wave called a Faraday wave, named after Michael Faraday who first described them. You've all probably seen standing waves, which are waves that remain in one place, while watching the waves on a lake on a windy day or surfers. Faraday waves are a different because they're nonlinear and can't be described as just the sum of their parts. Chaos theory is sometimes used as a term for nonlinear systems.
Now you know the sum total of my knowledge on Faraday waves. If there are any physicists who read this site, maybe they'll chime in with a more cogent explanation. Thankfully, you don't have to be a chaos theorist or a physicist in order to appreciate their beauty.
Is this is something that with not too much work can be done at home. Here's another video of Faraday waves from a different source (I wish people would at least credit these videos so one could tell where they came from). The title for this says the frequency used was 80Hz.