$(d_k(i,j,t))_{1\leq k\leq K}$, called *explicative variables*. These variables are here: $d_1$, the *density*, i.e. the average $\delta$ around a cell $(i,j)$ in a circular neighborhood of radius $\rho$; $d_2$, the Euclidean *distance* of a cell to the nearest road; $d_3$ the *network-distance* of a cell to the nearest city center, i.e. the sum of $d_2$ and edge lengths; and $d_4$, the *accessibility* of activities (or rather difficulty thereof), written $$d_4(i,j,t)=\left(\frac{1}{a_{\max}}\sum_{a=1}^{a_{\max}}d_3(i,j,t;a)^{p_4}\right)^{1/p_4}$$ where $d_3(i,j,t;a)$ is the network-distance of the cell to the nearest center with an activity $a$, and $p_4\geq1$ (typically 3) defines a $p$-norm.

A set of weights $(\alpha_k)_{1\leq k\leq K}\in[0,1]^K$ is assigned to these variables to tune their respective influence on what we define as the net *land value* of a cell, as follows: $$v(i,j,t)=\frac{1}{\sum_k \alpha_k}\sum_{k=1}^K \alpha_k\;\frac{d_{k,\max}(t)-d_k(i,j,t)}{d_{k,\max}(t)-d_{k,\min}(t)}.$$

Houses are preferentially built where $v$ is high, i.e. $d_k$’s are low. Thus the evolution of the system proceeds in three phases at each time step: (a) all values $v(i,j)$ are updated, (b) among the cells that have the best values, $n$ new cells are randomly chosen and “built” (set to $\delta=1$); (c) for each built cell, if $d_2$ is greater than a threshold $\theta_2$ (maximum isolation distance), then that cell is directly 