Square lattice with periodic boundary conditions and two species with diffusion dynamics and annihilation reaction A + B -> 0.
Lattice of size 10'000 x 10'000 with initial density 1.0 with very long simulation time (using Fortran): animation
Custom size below. Note that JavaScript is slower than Fortran, hence the smaller lattices.
The slope is fitted on the last decade only (grey band), and never beyond the onset of finite-size effects (t ≈ 0.01 N2, red dotted line). The approach to the asymptotic value -0.5 is slow: the local slope is about -0.64 at t = 103, -0.58 at t = 104 and -0.53 at t = 105 (measured on a 4000 x 4000 lattice), so a large lattice is needed to get close to -0.5. A single run fluctuates by about ±0.03 to 0.05 around these values.
