Hello dear John Rigby,

Here is my approach of the "Karatay pattern", and some of my flight of fancy with the Penrose tillings.
Use the arrows to go upwards or backwards. If you click between the two arrows it open some shorcuts.
One more time i apologie for my bad english.

So,

At the begining it's always drawing by hand. Free hand on my little notebook (A6 side, white paper), while having a cofee in a nice bar (Paris is a very good city for bars).
Looking at your Figure 1 on the table.