Violence is quite non-differentiable. It breaks. It breaks bodies. It breaks relationships. Now, the concept of violence is subtly but strongly linked to the concept of time, like death. But often in the sciences, the dimension of the x-axis of a graph is time.
Violence is as opposed to curves. Subsequent curves may form a spiral. I would say that sex is the ultimate non-violent game, true violence being nonconsensual, except the ultimate desired release, when laid bare, is a very particular form of momentary loss also found with another illicit group.
Is violence discontinuous? I would go as out to say that it is not. The ultimate effect of violence, as best as we know it, is death. Death, however it may seem to us mere mortals, is not discontinuous but in memory over time. We affect the world. Then the world continues affecting the world regardless. In fact if you think about it, the only thing lost with death is memory.