Figure 4.

Integration. (a) System S analysed in this figure and in Figure 5. All units have $\tau =1$ and $\eta =0$ (partially deterministic MAJORITY gates). The remaining panels show on the top the time unfolded graph of different mechanisms constraining different output purviews and on the bottom the probability distributions (effect repertoires). The black bars show the probabilities when the mechanism is constraining the purview, and the white bars show the partitioned probabilities. The “*” indicates the state selected by the maximum operation in the ID function. (b) The mechanism $M=\{A,E\}$ in state $m=\{\uparrow ,\downarrow \}$ constraining the purview $Z=\{A,E\}$. While the complete partition has nonzero intrinsic information, the mechanism is clearly not integrated, as revealed by the MIP partition ${\psi }^{*}=\{(\{A,\},\left\{A\right\}),(\{E,\},\left\{E\right\})\}$, resulting in zero integrated information. (c) The mechanism $M=\{A,B\}$ in state $m=\{\uparrow ,\uparrow \}$ constraining the purview $Z=\{A,B\}$. The partition ${\psi }^{*}=\{(\{A,\},\{A,B\}),(\left\{B\right\},\{\varnothing \})\}$ has less intrinsic information than any other partition, i.e., it is the MIP of this mechanism, and it defines the integrated information as 0.36. (d) The mechanism $M=\{A,B,D\}$ in state $m=\{\uparrow ,\uparrow ,\downarrow \}$ constraining the purview $Z=\{E,F\}$. The tri-partition ${\psi }^{*}=\{(\left\{A\right\},\{\varnothing \}),(\{\varnothing ,\},\left\{F\right\}),(\{B,D\},\left\{E\right\})\}$ is the MIP and it shows that the mechanism is not integrated, i.e, the mechanism has zero integrated information.