  We propose lacunarity as a novel recurrence quantification measure and
illustrate its efficacy to detect dynamical regime transitions which are
exhibited by many complex real-world systems. We carry out a recurrence plot
based analysis for different paradigmatic systems and nonlinear empirical data
in order to demonstrate the ability of our method to detect dynamical
transitions ranging across different temporal scales. It succeeds to
distinguish states of varying dynamical complexity in the presence of noise and
non-stationarity, even when the time series is of short length. In contrast to
traditional recurrence quantifiers, no specification of minimal line lengths is
required and rather geometric features beyond linear structures in the
recurrence plot can be accounted for. This makes lacunarity more broadly
applicable as a recurrence quantification measure. Lacunarity is usually
interpreted as a measure of heterogeneity or translational invariance of an
arbitrary spatial pattern. In application to recurrence plots, it quantifies
the degree of heterogenity in the temporal recurrence patterns at all relevant
time scales. We demonstrate the potential of the proposed method when applied
to empirical data, namely time series of acoustic pressure fluctuations from a
turbulent combustor. Recurrence lacunarity captures both the rich variability
in dynamical complexity of acoustic pressure fluctuations and shifting time
scales encoded in the recurrence plots. Furthermore, it contributes to a better
distinction between stable operation and near blowout states of combustors.
