What happens when spreading isn’t linear? We explore superdiffusion, where the mean-squared displacement grows with time faster than normal diffusion (an alpha between 1 and 2). From atmospheric turbulence to cellular transport and cosmic mixing, we trace the phenomenon, its historical roots, and the cutting-edge math—renormalization and the first rigorous proofs in turbulent models—that finally give it a solid foundation and reveal its real-world implications.

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