With equal probabilities, the Random Algorithm for the IFS with these rules
| T3(x, y) = (x/2, y/2) + (0, 1/2) | T4(x, y) = (x/2, y/2) + (1/2, 1/2) |
| T1(x, y) = (x/2, y/2) | T2(x, y) = (x/2, y/2) + (1/2, 0) |
fills in the unit square uniformly.
The pictures below were generated with these probabilities
p1 = 0.1, p2 = p3 = p4 = 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.
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