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Infinitesimal perturbations in various systems showing spatiotemporal chaos(STC) evolve following the power laws of the Kardar-Parisi-Zhang (KPZ)universality class. While universal properties beyond the power-law exponents,such as distributions and correlations, and their geometry dependence, areestablished for random growth and related KPZ systems, the validity of thesefindings to deterministic chaotic perturbations is unknown. Here we fill thisgap between stochastic KPZ systems and deterministic STC perturbations byconducting extensive simulations of a prototypical STC system, namely thelogistic coupled map lattice. We show that the perturbation interfaces, definedby the logarithm of the modulus of the perturbation vector components, exhibitthe universal, geometry-dependent statistical laws of the KPZ class, despitethe deterministic nature of STC. We demonstrate that KPZ statistics for threeestablished geometries arise for different initial profiles of theperturbation, namely point (local), uniform, and "pseudo-stationary" initialperturbations, the last being the statistically stationary state of KPZinterfaces given independently of the Lyapunov vector. This geometry dependencelasts until the KPZ correlation length becomes comparable to the system size.Thereafter, perturbation vectors converge to the unique Lyapunov vector,showing characteristic meandering, coalescence, and annihilation of borders ofpiece-wise regions that remain different from the Lyapunov vector. Our workimplies that the KPZ universality for stochastic systems generallycharacterizes deterministic STC perturbations, providing new insights for STC,such as the universal dependence on initial perturbation and beyond.

Initial perturbation matters: implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos