The actomyosin cortex is an active material that provides animal cells with a strong but flexible exterior, whose mechanics, including non-Gaussian fluctuations and occasional large displacements or cytoquakes, have defied explanation. We study the active nanoscale fluctuations of the cortex using high-performance tracking of an array of flexible microposts adhered to multiple cultured cell types. When the confounding effects of static heterogeneity and tracking error are removed, the fluctuations are found to be heavy-tailed and well-described by a truncated L\'evy stable distribution over a wide range of timescales and multiple cell types. Notably, cytoquakes appear to correspond to the largest random displacements, unifying all cortical fluctuations into a single spectrum. These findings reinforce the cortex's previously noted similarity to soft glassy materials such as foams, while the form of the fluctuation distribution will constrain future models of the cytoskeleton.

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