We compare and contrast three different, but complementary views of "structure" and "pattern" in spatial processes. For definiteness and analytical clarity we apply all three approaches to the simplest class of spatial processes: one-dimensional Ising spin systems with finite-range interactions....

It has been well-known since the pioneering work of Claude Shannon in the 1940s that a message transmitted with optimal efficiency over a channel of limited bandwidth is indistinguishable from random noise to a receiver who is unfamiliar with the language in which the message is written. In this...