Suppose you took an $n \times n$ array of cells, and for each cell there is a 0.5 probablity of being shaded or not. Suppose we defined "connected regions" as regions for which all shaded cells shared at least one edge (i.e. cells sharing corners are NOT connected), what would be the distribution of areas of connected shaded regions? What if the topology of the plot was toroidal i.e. regions on the edges would be connected?
Note: I do not have much experience with probability or percolation theory, so I would also appreciate any recommendations on resources I could use to answer more questions like this. Thanks!