If I want to have my cube (10 high, 30 wide, 20 deep) wave like a flag, I just take an image, and then use the wave effect as an unmask. We have all seen the flapping flag demo.
To get a left-right wave, I use the "overlaid z" render style. Front-back wave is created by using the "overlaid X" render style.
What is I want my waves to come from the center of the matrix and ripple outward like water drops? What if I want my waves to move at a 45-degree angle or rotating angle?