  Crowd behaviour challenges our fundamental understanding of social phenomena.
Involving complex interactions between multiple temporal and spatial scales of
activity, its governing mechanisms defy conventional analysis. Using 1.5
million Twitter messages from the 15M movement in Spain as an example of
multitudinous self-organization, we describe the coordination dynamics of the
system measuring phase-locking statistics at different frequencies using
wavelet transforms, identifying 8 frequency bands of entrained oscillations
between 15 geographical nodes. Then we apply maximum entropy inference methods
to describe Ising models capturing transient synchrony in our data at each
frequency band. The models show that 1) all frequency bands of the system
operate near critical points of their parameter space and 2) while fast
frequencies present only a few metastable states displaying all-or-none
synchronization, slow frequencies present a diversity of metastable states of
partial synchronization. Furthermore, describing the state at each frequency
band using the energy of the corresponding Ising model, we compute transfer
entropy to characterize cross-scale interactions between frequency bands,
showing 1) a cascade of upward information flows in which each frequency band
influences its contiguous slower bands and 2) downward information flows where
slow frequencies modulate distant fast frequencies.
