Landscape as a Model: The Importance of Geometry
Figure 3
The distribution of step lengths possible in five virtual landscapes. The von Neumann (orange, at 1.0) and hexagonal (green, at 1.074 km) landscapes only allow a single step length, whereas the Moore geometry allows two steps (red, at 1.0 and 1.41). A single instance of a Dirichlet landscape (blue, mean 1.095 km, gamma distributed with shape = 1.98, rate = 1.8 × 104) allows a distribution of step lengths that vary from parcel to parcel but have a mean similar to the hexagonal geometry. Other irregular landscapes have step length distributed similarly (CGD4 shown, blue dashed line, mean 1.15 km).