  We consider one dimensional lattice diffusion model on a microscale grid with
many discrete diffusivity values which repeat periodicially. Computer algebra
explores how the dynamics of small coupled `patches' predict the slow emergent
macroscale dynamics. We optimise the geometry and coupling of patches by
comparing the macroscale predictions of the patch solutions with the macroscale
solution on the infinite domain, which is derived for a general diffusivity
period. The results indicate that patch dynamics is a viable method for
numerical macroscale modelling of microscale systems with fine scale roughness.
Moreover, the minimal error on the macroscale is generally obtained by coupling
patches via `buffers' that are as large as half of each patch.
