Write a programme to sequentially occupy random sites on a 2-D square lattice with each site occupied with a probability p . Identify and record cluster formation (ie new occupied site has at least one neighbour site occupied) and also cluster bridging where the occupation of a given site links two (or more) clusters. Percolation occurs when a single cluster spans the lattice, i.e. touches all four edges. Reproduce Figure 7.26 and show how to estimate the smallest probability at which a spanning cluster will form (the critical probability, pc)

Random Fire burn-out time 100 80- lattice size = 50 x 50 60 40 20 ,0 .o 0.6 0.8 0.4 site concentration 0.2