10 1 10 2 10 3 10 4 1E-3 0.01 0.1 1 k  = 10 k  = 1 e$_{ = 3.00}$ e$_{ = 0.05}$ e$_{ = 0.00}$ q  = 10 <  G > /  q F Area FIG. 5: Culture-area relationship for q = 10 and different values of ϵ . In circles are included the calculations for the corresponding value of ϵ indicated with labels. In square are represented the calculations done according to the relation ϵ = k ( L − 5), with the value of k indicated with a label. F = 3, L = 50 and 200 different random initial conditions were used. The area is obtained according to A = L $^{2}$. system to a monoculture state for even higher values of r . Finally, we study the influence of the Mass Media in the culture-area relation when the interaction on the society is social. An extensive examination of the culture-area relation on the Axelrod model with dyadic interaction was done in Ref. [30]. The authors obtained a non-monotonic behavior for the culture-area relation for q values below the critical value where the transition occurs ( q < q$_{c}$ ) while for q > q$_{c}$ the number of cultures G first increases in a power-law dependence as G ∼ A x with x = 1 and then gradually flattens when the area becomes of the order of the maximum number of cultures q $^{F}$. In the limit L → ∞ there are only two possible outcomes: for q < q$_{c}$ a single culture dominates in an ordered regime, while G → q F and all the cultures are represented in the network in a full disordered regime. The authors proved the transition between these two regimes to be discontinuous because G jumps from 1 to q F at q = q$_{c}$ . Contrarily, when the model is changed including instead of dyadic interaction social influence, Ref. [21], the problematic result of the Axelrod model which produces a multicultural final state only for small societies [30] is overcome and only 16