be known in advance and are therefore essential to monitor.

#### Morphology

To assess the morphological structure of an urban configuration, we map it onto a 2D metric space defined by a pair of global indicators $(D,I)$ called the *integrated density* and the *Moran index* (Fig. \[fig\_morpho\]). The density $D\in[0,1]$ is calculated by taking the $p$-norm (with exponent $p_D\geq 1$, typically 3) of the local densities $d_1$: $$D(t)=\left(\frac{1}{\sum_{i,j} \delta(i,j,t)}\!\!\sum_{\scriptstyle i,j=1\atop\scriptstyle\delta(i,j,t)\neq0}^N\!\!d_1(i,j,t)^{p_D}\right)^{1/p_D}$$ Moran’s $I$, an index of spatial autocorrelation, is widely used in quantitative geography [@tsai2005quantifying; @lenechet:hal-00696445] to evaluate the “polycentric” character of a distribution of populated cells. It is defined by $$I(t)=\frac{M^2}{\sum_{\mu\neq\nu} 1/d_{\mu\nu}}\frac{\sum_{\mu\neq\nu} (P_\mu-\overline{P})(P_\nu-\overline{P})/d_{\mu\nu}}{\sum_{\mu=1}^{M^2}(P_\mu-\overline{P})^2}$$ where the lattice is partitioned into $M\times M$ square areas, at an intermediate scale between cell size and world size ($1\ll\!M\ll\!N$), $d_{\mu\nu}$ is the distance between the centroids of areas $\mu$ and $\nu$, $(P_\mu)_{1\leq\mu\leq M^2}$ denotes the number of occupied cells in each area, and $\overline{P}$ is their global average. We can recognize in this formula the normalized ratio of a modified covariance (pairwise correlations divided by distances) and the variance of the distribution. Moran’s $I$ belongs by construction to the interval $[-1,1]$, where values near 1 correspond to a strong monocentric distribution, values around 0 to 