Information integration as a function of modularity – homogeneity. Values of Φ were obtained from Gaussian Toeplitz connection matrices (n = 8) with a fixed amount of total synaptic weight (self-connections allowed). The plot shows Φ as a function of the standard deviation σ of the Toeplitz connection profile. Connection matrices (cases a to f) are shown at the left, for different values of σ. For very low values of σ (σ = 0.001, case a), Φ is zero: the system is made up of 8 causally independent modules. For intermediate values of σ (σ ≈ 0.01 to 0.1, cases b, c, d, e), Φ increases and reaches a maximum; the elements are interacting in a heterogeneous way. For high values of σ (σ = 1, case f) Φ is low; the interactions among the elements are completely homogeneous.