Turbulent convection efficiently transports energy up to the solar photosphere, but its multi-scale nature and dynamic properties are still not fully understood. Several works in the literature have investigated the emergence of patterns of convective and magnetic nature in the quiet Sun at spatial and temporal scales from granular to global. Aims. To shed light on the scales of organisation at which turbulent convection operates, and its relationship with the magnetic flux therein, we studied characteristic spatial and temporal scales of magnetic features in the quiet Sun. Methods. Thanks to an unprecedented data set entirely enclosing a supergranule, occurrence and persistence analysis of magnetogram time series were used to detect spatial and long-lived temporal correlations in the quiet Sun and to investigate their nature. Results. A relation between occurrence and persistence representative for the quiet Sun was found. In particular, highly recurrent and persistent patterns were detected especially in the boundary of the supergranular cell. These are due to moving magnetic elements undergoing motion that behaves like a random walk together with longer decorrelations ($sim2$ h) with respect to regions inside the supergranule. In the vertices of the supegranular cell the maximum observed occurrence is not associated with the maximum persistence, suggesting that there are different dynamic regimes affecting the magnetic elements.
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