In this thesis, we investigate the spreading of a localized perturbation in a reversible (2+1)-dimensional cellular automaton on a hexagonal lattice as a macroscopic analogue of the butterfly effect in many-body systems. The spatiotemporal extent of the perturbation is characterized by the chaos front, whose statistical properties are analyzed within the framework of interface growth phenomena. Using numerical simulations, we determine the critical exponents, examine finite-size and finite-time corrections, and compare the results with discrete models of known universality. We provide empirical evidence that the morphology of the chaos front belongs to the (1+1)-dimensional Kardar–Parisi–Zhang universality class for flat initial conditions. In particular, we extract the ballistic propagation velocity, demonstrate that the front fluctuations exhibit the expected scaling behavior, and show that the noise distribution is described by the Tracy–Widom distribution of the Gaussian Orthogonal Ensemble.
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