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Rate maps quantify the variability of surface rates during the dissolution of crystalline matter. Recently, highly spatially resolved rate maps revealed the existence of rhythmic pulses of the material flux from the crystal surface. The mechanism underpinning this behavior is not yet understood but the two potential influencing factors are surface-controlled or transport-controlled conditions that may govern the resulting pulsating reaction kinetics in the system. In this study, we apply two numerical methods to identify the dominating mechanism of pulsating dissolution. First, the influence of solute transport is simulated using a reactive transport model (RTM), which yields dissolution rates and concentration distribution due to the flow field, i.e., extrinsic reactivity. Second, the influence of intrinsic surface reactivity inherent to the material is simulated using kinetic Monte Carlo (KMC) simulations, where the distribution of reactive sites over time is observed on an atomic scale. Local dissolution rates can be reproduced with RTM, but no kinetically effective periodic changes of the concentration gradients can be observed and no new dissolution pulses are generated. Control via periodic changes in extrinsic reactivity is thus ruled out as a governing mechanism. In contrast, pulsating dissolution is clearly observed in KMC simulation, leading to the conclusion that the self-assembly of varying reactive surface building blocks causes the pulsating dissolution. The simulation results suggest that etch pits generate regions with a high number of steps of single crystal layers and, consequently, with sites of increased reactivity at periodic intervals. These steps move over the crystal surface outward from the pit center and are followed by a region with a low number of surface steps. Only when the steps reach a certain spacing to the center new steps are generated at the transition between the hollow core and the etch pit. This self-assembly is observed as a fundamental behavior of crystalline dissolution in KMC models, without any additional parametrization. It thus represents a fundamental mechanism in crystal dissolution and should be considered for an accurate atomic understanding of crystal dissolution.