Suppose we tile the plane randomly with black and white unit square tiles in a grid pattern, black and white tiles occuring with equal probablity (sort of like the static you used to see on your old black and white TV). Consider the polyominoes formed by connecting like-colored tiles along their edges. Since every possible coloring of an nxn subsquare should occur, I'm thinking that every finite polyomino should occur in every orientation. What is the probability that a randomly chosen square is in a unomino (I find only one page on the web with that word!)? What is the probability that a randomly chosen polyomino is a unomino? What is the most frequent polyomino in both senses? I am thinking that if black squares occur with probability 1/2, the probability of an infinite polyomino is 0. Certainly if they occur with probability 1, the probability of an infinite polyomino is 1. What about choosing black squares with probability 3/4? Other probabilities? - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"