Oops. I didn't see that you had linked an article. I thought you were asking for the answer.

So ... number of lattice points inside a circle of radius r=vt? where v is the speed of the fire and t is time. That is roughly (pi*r^2)/(vol) + small error, where vol is the volume of a lattice cell. The error term is interesting and I think you may be able to find in the lit for some lattices.