  The exact order of mixing for zero-dimensional algebraic dynamical systems is
not entirely understood. Here non-Archimedean norms in function fields of
positive characteristic are used to exhibit an asymptotic shape in non-mixing
sequences for algebraic $Z^2$-actions. This gives a relationship between the
order of mixing and the convex hull of the defining polynomial. Using these
methods, we show that an algebraic dynamical system for which any shape of
cardinality three is mixing is mixing of order three, and for any $k\ge1$
exhibit examples that are $k$-fold mixing but not $(k+1)$-fold mixing.
