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According to the standard model of cosmology, the arrangement of matter in the cosmos on scales much larger than galaxies is entirely specified by the initial conditions laid down during inflation. But zooming in by dozens of orders of magnitude to microscopic (and human?) scales, quantum randomness reigns, independent of the initial conditions. Where is the boundary of determinism, and how does that interplay with chaos? Here, we make a first attempt at answering this question in an astronomical context, including currently understood processes. The boundary is a function, at least, of length scale, position, and matter type (dark matter being more simply predictable). In intergalactic voids, the primordial pattern of density fluctuations is largely preserved. But we argue that within galaxies, the conditions are at minimum chaotic, and may even be influenced by non-primordial information, or randomness independent of the initial conditions. Randomness could be supplied by events such as supernovae and jets from active galactic nuclei (AGN) and other accretion disks, which, with the help of chaotic dynamics, could broadcast any possible microscopic randomness to larger scales, eventually throughout a galaxy. This may be generated or amplified by a recently investigated process called spontaneous stochasticity, or effective randomness in turbulent systems arising from arbitrarily small perturbations.