  We devise a new 1D atomistic scale model of vicinal growth based on Cellular
Automaton. In it the step motion is realized by executing the automaton rule
prescribing how adatoms incorporate into the vicinal crystal. Time increases
after each rule execution and then nDS diffusional updates of the adatoms are
performed. The increase of nDS switches between the diffusion-limited (DL,
nDS=1) and kinetics-limited (KL, nDS >> 1) regimes of growth. We study the
unstable step motion by employing two alternative sources of instability -
biased diffusion and infinite inverse Ehrlich-Schwoebel barrier (iiSE). The
resulting step bunches consist of steps but also of macrosteps since there is
no step-step repulsion incorporated explicitly into the model. This complex
pattern formation is quantified by studying the time evolution of the bunch
size N and macrostep size Nm in order to find the proper parameter combinations
that rescale the time and thus to obtain the full time-scaling relations
including the pre-factors. For the case of biased diffusion the time-scaling
exponent beta of N is 1/2 while for the case of iiSE it is 1/3. In both cases
the time-scaling exponent beta_m of Nm is ~3beta/4 in the DL regime and 3beta/5
in the KL one.
