Exploring 2-dimensional elastic collisions between equal circular bodies. The red and blue data to the right represents vector magnitude of each body; the purple is the magnitude of the sum vector.
At first glance, it would appear that the law of conserved kinetic energy is getting violated, but as far as I understand, it's just the bouncing off the unmoving walls that make it appear that way. Maybe someone with a better understanding of the physics and math involved could elaborate.