Inverse Tree

This is a classic IFS series (x_n+1,y_n+1) = f(x_n,y_n).

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))
The range of f(x,y) or 0 to 1 on both axes.