Fig. 4.

Emergent relations between perimeter quantities and forest area $[\mathrm{F}]$: (A–C) forest perimeter $[\mathrm{FG}]$ and grassland-weighted forest perimeter ${〈[\text{FG}]〉}_{\text{cg}}$, (D–F) forest gain terms and loss terms in Eqs. 5 and 8, (G–I) forest area rate of change $(\mathrm{d}/\mathrm{d}t)[\mathrm{F}]$ from Eq. 9. Columns correspond to vertical dashed lines in Fig. 2 ($\varphi N=0.257,\varphi N=0.38,\varphi N=1.32$). Domain size: 100 $\times$ 100 cells.