Figure 1.

Schematic of the $\mathrm{\Phi }\text{ID}$ approach to causal emergence. (a) Lattice of $\mathrm{\Phi }\text{ID}$ information atoms, with atoms corresponding to causal decoupling ($\mathcal{G}$) and downward causation ($\mathcal{D}$) highlighted. (b) Relationship between system variables ${\mathit{X}}_t$, supervenient variables $V_t$ and emergent properties (cf. equation (3.2)). Images adapted from [7,27,28]. (Online version in colour.)