Two cities with the same average population density can look completely different: one is a uniform grid of blocks, the other a labyrinth of narrow alleys. The same goes for gravity: two central configurations of 5000 particles with nearly identical global clustering measures — variety (differing by only 1.686%)—turned out to be radically different inside. Variety grows in both directions from the Janus point (the moment of minimal system size) and serves as an indicator of the gravitational arrow of time in Barbour's approach. But why is that not enough?

To probe the local geometry, the researchers introduced the six-nearest-neighbor anisotropy A6. For each particle, they looked at how evenly its neighbors are distributed: 0 means they surround it equally from all sides, 1 means they are almost in a line. The average A6 for the first configuration is 0.1331, an almost isotropic background. For the second, it is 0.3419, a difference of 156.8%. In the first, no particle had A6 above 0.5; in the second, 18.1% did — entire regions of elongated structures. So the global variety measure misses the details of internal organization: two 'cities' with the same average density can be either a quiet suburb or a tangle of congested highways. To understand their evolution, you need to look at the geometry of the streets.