The next urban growth step is defined though the dynamics of new spreading centers. As the name indicates, this step determines whether any of the new, spontaneously urbanized cells will become new urban spreading centers. The global parameter, breed_coefficient, defines the probability for each new urbanized cell U(i,j,t+1) to become a new spreading center U'(i,j,t+1), given two neighboring cells also are available for urbanization
(2) U'(i,j,t+1) = f2[ breedcoefficient, U(i,j,t+1), random ],
where (k,l) are nearest neighbors to (i,j). If the cell is allowed to become a spreading center, two additional cells adjacent to the new spreading center cell also have to be urbanized. Thus an urban spreading center is defined as a location with three or more adjacent urbanized cells. The actualization of this step is dependent upon the slope_coefficientweighted topography and the availability of neighborhood cells to make the transition.
New Spreading Center
Growth: 

New spreading center growth example and pseudo code. 
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