Convergence of Deterministic IFS

Next, note

S3 ⊆ S2 = (S2)0,

To be sure S3 is thickened enough to cover all of S2, note we must cover the upper right corners of S2. To do this, thickening S3 by 1/8 suffices. That is,

S2 ⊆ (S3)1/8,

Consequently, h(S2, S3) = 1/8.

Return to Hausdorff Distance Convergence Example.