Convergence of Deterministic IFS

Next, note

S2 ⊆ S1 = (S1)0,

To be sure S2 is thickened enough to cover all of S1, note we must cover the upper right corners of S1. To do this, thickening S2 by 1/4 suffices. That is,

S1 ⊆ (S2)1/4,

Consequently, h(S1, S2) = 1/4.

Return to Hausdorff Distance Convergence Example.