Figure 1.

Visual representation of the relationships between PID and ΦID atoms for bivariate systems. In both cases, to aid visualization, atoms are arranged into a lattice, a mathematical construct which represents a hierarchical organization of information content, such that redundant information (held by every variable) is at the bottom and synergistic information (held only by the whole) is at the top. Please note that while here we focus in the case of two source variables, this information decomposition can be carried out over an arbitrary number of sources—which leads to a more elaborate lattice. For details of this more general construction we refer the reader to Williams (2011).