out of the scope of this paper.

Results {#sec_results}
=======

Our hybrid network/grid model was implemented in NetLogo [@NetLogo]. Plots and charts were created in R [@R] from exported data. Processing of GIS Data (for vectorization by hand of simple raster data) was done in QGIS [@QGIS_software]. Exploration of the 4D space of explicative variables’ weights $\alpha_k$ was conducted inside the $[0,1]^4$ hypercube with a linear increment of 0.2. This created $6^4-1=1295$ points, from $(0,0,0,0)$ excluded to $(1,1,1,1)$ included, via $(0.2,0,0,0)$, etc. Unless otherwise noted, the output values of the evaluation functions were averaged over 5 simulations for each combination of the $\alpha_k$’s.

Generation of urban patterns: validation of the model {#sec_extval}
-----------------------------------------------------

#### Typical patterns

We ran the model on different initial configurations, in which a few city centers $C_0$ (typically 4) were randomly positioned on a $56\times 56$ lattice, and their activity values drawn in $[1,a_{\max}]$ (both uniformly). The initial network $G_0$ was built progressively and quasi deterministically over increasing distances, by creating isolated clusters and linking them until they percolated into one component. The initial grid was empty ($\delta=0$ everywhere). Simulations were cut off at 30 iterations ($T=30\tau$), before the sprawl of urban settlements reached the square 