where G ( s N ) is a vector pointing in the direction of maximum cell density, defined as G ( s N ) = ∑ ∑ r ′ ∈ ∈ N ( r ′ − − r ) n ( s N r ′ ) , where s N r ′ is the configuration of the lattice site r ′ within the neighborhood N , and J ( s O ) is the momentum of the post-reorientation configuration, defined as J ( s O ) = ∑ ∑ j = 1 b s j O c j . This transition probability favors post-reorientation configurations with cells moving towards the cell density gradient.