Figure 4

The circannual waves of crime travel across the city. To examine the local-level waves of crime from a global perspective, we count the proportional number of regions that exhibit a statistically significant band b at the time step t in each city (i.e., the composed scale-averaged power \({\smash{C}_{c}^{b}(t)}\)). In the case of the circannual band, \({\smash{C}_{c}^{b}(t)}\) presents a typical value without much variability throughout the time series, suggesting a possible equilibrium at city level (shown in (A) for selected cities). However, the number of weeks Δt that each region keeps this period continuously follows a probability distribution (B) that decays far before the complete criminal series, implying that these waves move across the city. Such continuous movement supports the view of cities in disequilibrium. In the plots, the legend in (B) also applies to the curves in (A). Normalised time refers to the proportional amount of time to the whole time series