Start from an arbitrary point x₀. On every step pick one map Wᵢ at random, weighted by its probability p, and set xₙ₊₁ = Wᵢ(xₙ). Plotting each point that lands the dense cloud converges onto the IFS attractor regardless of the start point.
W(x,y) = [a b; c d]·[x;y] + [e;f]
Drag on the canvas to reseed x from the point under the cursor — the attractor snaps back to the same shape, since all the maps are contractive (Banach fixed-point theorem).