Figure 10. Space and Direction from a Fixed Point in Multiple Irregular Landscapes.

(A) A single Dirichlet landscape showing three fixed points (+). One (top left) occupies a cell inland, while another (top right) occupies a coastal cell that is restricted by the edge of the extent. The third (centre) is shown with the available directions for movement in that landscape instance.

(B) A second random instance of a Dirichlet tessellation in the same extent. The three fixed points are highlighted, with their respective cells and directions of movement.

(C) The sum of the observations of space and direction around the three points after only five Dirichlet landscapes. Light grey lines indicate the boundaries of cells in all five landscapes. The kernel associated with inland and coastal points is shown in shades of grey, with the lightest shade showing an area only associated with the point in one landscape instance and black being the area common to all five. Although clearly not circular, given enough iterations, all points approach a circular kernel of influence unless restricted by the extent. Available directions for movement across all five landscapes are shown from the third point, demonstrating that movement in any direction is equally possible.