a bit weird that the PhysicsSE post doesn't even state the lattice automaton rules, how is any answer reasonably expected without a clear system statement?

without a clear statement of phenomenology (which "velocity" and what "acceleration" is the question about? numerous similar effects can be known but no reasonable answer can be given without stating the system update rules...

For example to me this is reminiscent of Regge Calculus on some 2D patch of surface. Like what is the question?