'Memetic isolation' is a situation in which a society or culture exhibits a cultural trait not found in any neighbouring cultures (Gatherer 2002b). A previously developed simulation, consisting of a grid of connected societies of cultural agents, is further analysed to define the circumstances under which memetic isolation is maximised and minimized. Parameters varied include migration, and cultural interaction within and between societies. Some stereotypical societies are simulated, and the differences in outcomes are analysed statistically. A genetic algorithm is then used to discover the combinations of parameters that produce extreme results. Minimization of memetic isolation appears to be simply a matter of cultural or natural selection on the meme concerned. By contrast, maximization of memetic isolation requires an intuitively unlikely combination of low cultural interaction, high migration and no selection. The classic memetic theoretical result, that horizontally transmitted memes tend to be more spatially clustered than vertically transmitted memes or genes, is shown to depend on the existence of cultural bridges, or 'weak ties', between societies and also to be at the mercy of migration rates and selective forces.