Response to comment on "Decagonal and quasi-crystalline tilings in medieval islamic architecture"

Our study showed that both Gunbad-i Kabud and Darb-i Imam tessellations belong to a sequence of Islamic tilings that resolve into a common set of girih tiles, so local similarities are expected. However, historically accurate reconstructions show that Darb-i Imam is unique, the only known example that does not repeat periodically and that displays a self-similar transformation enabling its continuation ad infinitum to a perfect quasi-crystalline pattern.