Animation is a Markov stunt

Run the 5-tuples and make toroidal shapes, change curvatures and manage N density to simulae kinetic action.  N density has more action when high, low otherwise. But you will have amazing accura as long as you can move among the stable point. With a bi of relativity in the two extra deviations,  your 'snake' is very accurate, but your computer tired.  Making that snake enggae in  action like spin, crawl, spiral; and you can make the surface appear to be a leg walking.

But kinetics of the colored dots are handled exterior   Mostly that means renormalizing N density, especially where action is happening. Re-normalize means to resolve the kinetic deviations down to the integer.