Boundary Diagrams

I've created a series of Self-Similar Boundary diagrams. I'm using original self-similar tile sets as the structure for these dot pattern diagrams. I begin the process of creating each diagram by designing a self-similar tile set. Then I create a tiling that emphasizes the transition from the largest tile to a potentially infinite boundary. Finally I generate vertices and extrinsic vertices for the tiling. The vertices or dot pattern recedes from open to closed at the boundary. I've included images of the dot pattern and the tiling structure for the vertices.