River meander planforms can be described based on wavelet analysis, but an objective method to identify the main characteristics of a meander planform over all spatial scales is yet to be found. Here we show how a set of simple metrics representing meander shape can be retrieved from a continuous wavelet transform of a planform geometry. We construct a synoptic multiple looping tree to establish the meander structure, revealing the embedding of dominant meander scales in larger-scale loops. The method can be applied beyond the case of rivers to unravel the meandering structure of lava flows, turbidity currents, tidal channels, rivulets, supraglacial streams, and extraterrestrial flows.