The forest's always greener when it's not on fire

Classical Mechanics Level pending

In the model referenced in the text, trees are planted at the rate p p and have a density ρ tree \rho_\textrm{tree} on the 2D lattice. Find the average number of new trees that are planted at each timestep.

( 1 ρ tree ) × p × L 2 \left(1-\rho_\textrm{tree}\right)\times p\times L^2 ρ tree × ( 1 ρ tree ) × p × L 2 \rho_\textrm{tree}\times \left(1-\rho_\textrm{tree}\right)\times p\times L^2 ρ tree × p × L 2 \rho_\textrm{tree}\times p\times L^2

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