Sample eigenvalue spacings from GUE (Gaussian Unitary Ensemble) and GOE (Orthogonal). The Wigner surmise predicts the spacing distribution: P(s) ~ s·e^(-πs²/4) for GUE. This repulsion between levels is universal — it appears in nuclear spectra, quantum chaos, and even prime gaps.
Wigner: P(s) = (π/2)s·exp(−πs²/4) [GUE: (32/π²)s²·exp(−4s²/π)] | Poisson: P(s) = e^{−s}