Spatial Dynamics - Continuous case

When analysing the process of spatial growth for continuous phenomena, one should consider not only the spatial expansion of a phenomenon in terms of presence or absence of its properties, but also the change of intensity throughout time. In each location of space, the intensity value can either increase or decrease at successive moments of the diffusion process. Therefore, for continuous phenomena, the binary concept of presence/absence can be replaced by another one called densification.

The concept of a phenomenon spreading through geographic space is considered in many diverse subject areas like the spread of wildfires, urban growth, infection diseases spread, diffusion of innovation, and ripple effects in the natural world.

In 1969, Peter Gould published a synthetic paper that clarifies the understanding of spatial diffusion processes, with clear distinctions between diffusion types and definitions of basic concepts (Gould 1969) (Abler R. et al. 1972). Spatial expansion and densification can be modelled according to the following concepts.

Spatial diffusion can be classified into three categories that represent the characteristics of the spread; we divide them in two groups: spatially dependant and non-spatially dependant diffusion.