This is a classic IFS series (xn+1,yn+1) = f(xn,yn).
f(x,y) is chosen from one of the following with equal probability. f(x,y) = (x/2,y/2) f(x,y) = (1/(x+1),y(y+1)) f(x,y) = (x/(x+1),1/(y+1))