(iii) Edge Growth

Edge-growth dynamics define the part of the growth that stems from existing spreading centers. This growth propagates both the new centers generated in step ii in this time step, time (t+1), and the more established centers from earlier times. Thus, if a non-urban cell has at least three urbanized neighboring cells, it has a certain global probability to also become urbanized defined by the spread_coefficient, given it is possible to build on the cell (slope_coefficient). Thus this edge growth can be expressed by

(3) U(i,j,t+1) = F3[ spread_coefficient, slope_coefficient, U(i,j,t), U(k,l), random ],

where (k,l) belongs to the nearest neighborhood of (i,j).

	Edge Growth: F(spread_coefficient, slope_coefficient) { for (all non-edge pixels (i,j)) if ((i,j) is urban) and (random_integer < spread_coefficient) if (at least two urban neighbors exist) if (a randomly chosen, non-urban neighbor is available for urbanization) (i,j) neighbor = urban } end edge growth
Edge growth example and pseudo code.