Calculating integrated information — partitions, MIB, and cause-effect structure
Computing Φ requires evaluating every possible bipartition of the system to find the Minimum Information Bipartition (MIB) — the cut that reduces cause-effect power the least. Φ = min over all bipartitions of φ_partition, where φ_partition measures the Earth mover's distance (or KL divergence) between the cause-effect structure of the whole versus the sum of its parts. This is #P-hard in general (exponential in N). The visualization shows: the TPM (transition probability matrix) encoding the system's causal structure, each bipartition's information loss, and the MIB highlighted in gold. Real Φ calculation is intractable for N>8; this uses a principled proxy.