  We study the growth of norms of ergodic integrals for the translation action
on spaces coming from expansive, self-affine Delone sets. The linear map giving
the self-affinity induces a renormalization map on the pattern space and we
show that the rate of growth of ergodic integrals is controlled by the induced
action of the renormalizing map on the cohomology of the pattern space up to
boundary errors. We explore the consequences for the diffraction of such Delone
sets, and explore in detail what the picture is for substitution tilings as
well as for cut and project sets which are self-affine. We also explicitly
compute some examples.
