Most of these figures exhibit at least two lines of symmetry, but there are a couple that only have one. What causes this behavior?
Different wavelengths?
I’d be quick to guess that in those cases, the missing axis of symmetry falls beyond the field of view. That is to say, it might not be trivial to align the focus of the vibration such that the center of each axis falls on the plate, and demonstrates a pattern depicting the perfect midpoint of the figure.
I've noticed patterns quite like these (viz. #5, 11-13) on the surface of beer in a pint glass. I've speculated it's the result of either the different sizes of bubbles or differing rates at carbonation sites, but I hadn't noticed the similarity to Chladni patterns.