The random is whatever we don’t know the cause of. Strictly speaking nothing is random, or ever can be random; every event has a proximate cause and more distant causes. When we talk about randomness we simply mean that we can’t sort out all the causes in some particular case. In art as in everything else, randomness is only apparent.
The arbitrary is a selection from a finite number of possibilities, all of which are equally good. All art is arbitrary in its origins, but I at least hope that it proceeds toward the necessary, toward one single best outcome.
The best word to describe the character of the forms that an “informel” or open-ended, moving abstraction makes is…I don’t know. Neither of the above.