(* this draws a random perculation 
grid with the given perameters*)

h=20; (* height*)
w=20;a (* width *)
p=.5;  (* probability of including edge*)
j=0; (*intial positions*)
k=0;
a={Line[{{0,0},{0,h},{w,h},{w,0},{0,0}}]};
For[j=0, j<h, j++, For[k=0,k<w,k++,
If[Random[]<p,  a=Append[a,Rectangle[{j,k},{j+1,k+1}]]]
]];
label=StringJoin["p = ", ToString[p]];
Show[Graphics[{a, Text[label,{w/2,-h/10}]}],  AspectRatio -> Automatic]