  Human mobility patterns are surprisingly structured. In spite of many hard to
model factors, such as climate, culture, and socioeconomic opportunities,
aggregate migration rates obey a universal, parameter-free, `radiation' model.
Recent work has further shown that the detailed spectral decomposition of these
flows -- defined as the number of individuals that visit a given location with
frequency $f$ from a distance $r$ away -- also obeys simple rules, namely,
scaling as a universal inverse square law in the combination, $rf$. However,
this surprising regularity, derived on general grounds, has not been explained
through microscopic mechanisms of individual behavior. Here we confirm this by
analyzing large-scale cell phone datasets from three distinct regions and show
that a direct consequence of this scaling law is that the average `travel
energy' spent by visitors to a given location is constant across space, a
finding reminiscent of the well-known travel budget hypothesis of human
movement. The attractivity of different locations, which we define by the total
number of visits to that location, also admits non-trivial, spatially-clustered
structure. The observed pattern is consistent with the well-known central place
theory in urban geography, as well as with the notion of Weber optimality in
spatial economy, hinting to a collective human capacity of optimizing recurrent
movements. We close by proposing a simple, microscopic human mobility model
which simultaneously captures all our empirical findings. Our results have
relevance for transportation, urban planning, geography, and other disciplines
in which a deeper understanding of aggregate human mobility is key.
