With equal probabilities, the Random Algorithm
for the IFS with these rules 
T_{3}(x, y) = (x/2, y/2) + (0, 1/2) 
T_{4}(x, y) = (x/2, y/2) + (1/2, 1/2) 
T_{1}(x, y) = (x/2, y/2) 
T_{2}(x, y) = (x/2, y/2) + (1/2, 0) 

fills in the unit square uniformly. 
The pictures below were generated with these probabilities 
p_{1} = 0.1, p_{2} = p_{3} = p_{4} = 0.3. 
Successive pictures show increments of 25000 points. With enough patience,
the whole square will fill in, but some regions fill in more quickly than others. 
