  We present a detailed clustering analysis of the young stellar population
across the star-forming ring galaxy NGC 6503, based on the deep HST photometry
obtained with the Legacy ExtraGalactic UV Survey (LEGUS). We apply a
contour-based map analysis technique and identify in the stellar surface
density map 244 distinct star-forming structures at various levels of
significance. These stellar complexes are found to be organized in a
hierarchical fashion with 95% being members of three dominant super-structures
located along the star-forming ring. The size distribution of the identified
structures and the correlation between their radii and numbers of stellar
members show power-law behaviors, as expected from scale-free processes. The
self-similar distribution of young stars is further quantified from their
autocorrelation function, with a fractal dimension of ~1.7 for length-scales
between ~20 pc and 2.5 kpc. The young stellar radial distribution sets the
extent of the star-forming ring at radial distances between 1 and 2.5 kpc.
About 60% of the young stars belong to the detected stellar structures, while
the remaining stars are distributed among the complexes, still inside the ring
of the galaxy. The analysis of the time-dependent clustering of young
populations shows a significant change from a more clustered to a more
distributed behavior in a time-scale of ~60 Myr. The observed hierarchy in
stellar clustering is consistent with star formation being regulated by
turbulence across the ring. The rotational velocity difference between the
edges of the ring suggests shear as the driving mechanism for this process. Our
findings reveal the interesting case of an inner ring forming stars in a
hierarchical fashion.
