  In order to study the unstable step motion on vicinal crystal surfaces we
devise vicinal Cellular Automata. Each cell from the colony has value equal to
its height in the vicinal, initially the steps are regularly distributed.
Another array keeps the adatoms, initially distributed randomly over the
surface. The growth rule defines that each adatom at right nearest neighbor
position to a (multi-) step attaches to it. The update of whole colony is
performed at once and then time increases. This execution of the growth rule is
followed by compensation of the consumed particles and by diffusional update(s)
of the adatom population. Two principal sources of instability are employed:
biased diffusion and infinite inverse Ehrlich-Schwoebel barrier (iiSE). Since
these factors are not opposed by step-step repulsion the formation of
multi-steps is observed but in general the step bunches preserve a finite
width. We monitor the developing surface patterns and quantify the observations
by scaling laws with focus on the eventual transition from diffusion-limited to
kinetics-limited phenomenon. The time-scaling exponent of the bunch size N is
1/2 for the case of biased diffusion and 1/3 for the case of iiSE. Additional
distinction is possible based on the time-scaling exponents of the sizes of
multi-steps, these are 0.36-0.4 (for biased diffusion) and 1/4 (iiSE).
