Although the Turing model and the Markov chain process are both ideal for studying systems which involve spatial interaction between adjacent sites, in practice interaction may occur across much larger spatial levels. Moreover, there is no reason why locations have to lie on a lattice structure, which has been our presumption so far in order to enable some degree of mathematical tractability. This chapter presents two extensions to earlier spatial analyses. The first introduces the concept of long-range dependence, whilst the second examines processes which develop over real, rather than discrete, space.