  We present limiting shape results for a non-abelian variant of the abelian
sandpile growth model (ASGM), some of which have no parallel in the ASGM. One
of our limiting shapes is an octagon. In our model, mass spreads from the
origin by the toppling rule in Zhang's sandpile model. Previously, several
limiting shape results have been obtained for the ASGM using abelianness and
monotonicity as main tools. As both properties fail for our model, we use a new
proof technique: in our main proof, we introduce several cellular automata to
mimic our growth model.
