I always get lost in my thoughts on the mechanical physics of how things work or how it would work. Well I have my coffee cup here full of coffee, I flicked it and watched the waves close into the centre almost perfectly. So I took a video and was surprised to see the circular waves from the edges of the cup somehow turn into seemingly perfect square form just before meeting in the centre. Does anyone know why this happens?
The perturbation you gave to the coffee cup in order to start the waves on their way towards the cup's center was not perfectly radially symmetric. This means the waves themselves weren't either (and will contain some higher harmonics that contain deep nulls at certain angles), but their non-circularity isn't obvious to begin with.
Now note that as the waves travel towards the center, the diameter of the waves shrinks and their amplitude grows, and any original noncircularity which was present when the waves originated will get magnified. Then, because the noncircular waves do not have the same wavelength as the circular ones, they will not get focused into a point.
Next, you should try generating circular waves by dropping a round object into the exact center of the cup and watching the waves radiate outward, bounce off the walls, and return to the center. the resulting "point" focus will probably be radially symmetric.