Most tessellations, especially in architecture, limit the available diversity within the chosen system. Part-to-whole relationships are singular when they could be scalable. Self-similarity solves the problem by allowing a potentially infinite range of parts within one whole. It's possible to design chaotic part-to-whole relationships that are flexible but impractical. Self-similarity restores the practicality while maintaining acceptable flexibility.
Other self-similar tile sets can be based on regular polygons including squares or hexagons. Here’s an animation using three scaled sets of three prototiles: http://joebartholomew.com/aniVertices_HSS9.html