Looking at the heritage of traditional Persian pentagonal patterns (patterns made from tiles derived from the pentagon), one can suppose that the artists, very early on, have set targets for their creation. One is the search for self-similarity; another is the search for methods of connection between the two main families of patterns. It is strange and intriguing that the historic artists did not fully achieved these targets. This chapter, following a previous publication (Castera, Nexus Netw J 18:223, 2016), proposes solutions and new developments. There are no Penrose patterns in that story; only binary tiling and the X-Tiles.