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We study nonequilibrium dynamics of SU(2) lattice gauge theory in Minkowskispace-time in a classical-statistical regime, where characteristic gluonoccupancies are much larger than unity. In this strongly correlated system farfrom equilibrium, the correlations of energy and topological densities showself-similar behavior related to a turbulent cascade towards higher momentumscales. We employ persistent homology to infer topological features of thegluonic plasma via a hierarchy of simplicial and cubical complexes. Alltopological observables under investigation are also manifestly gauge invariantand are shown to exhibit self-similar evolution, which relate the spatial andtemporal properties of the plasma in terms of universal scaling exponents andfunctions. The findings may help to understand the early stages of heavy-ioncollisions in the limit of high energies, and our methods can also facilitatethe topological analysis of other complex systems such as encountered inexperiments with ultracold quantum gases.

Probing universal dynamics with topological data analysis in a gluonic plasma