  We investigate the permissible growth rates of functions that are
distributionally chaotic with respect to differentiation operators. We improve
on the known growth estimates for $D$-distributionally chaotic entire
functions, where growth is in terms of average $L^p$-norms on spheres of radius
$r>0$ as $r \to \infty$, for $1 \leq p \leq \infty$. We compute growth
estimates of $\partial/ \partial x_k$-distributionally chaotic harmonic
functions in terms of the average $L^2$-norm on spheres of radius $r>0$ as $r
\to \infty$. We also calculate sup-norm growth estimates of distributionally
chaotic harmonic functions in the case of the partial differentiation operators
$D^\alpha$.
