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.
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.
I use my black fountain pen, no rule, no eraser. So it is a nice feeling
when all the lines turn to fit together.
Of course, i do not try to draw the interlaces (is it better to say "braids" ? ), which i consider as an embellishment.
Ok, it is a perfectible drawing, but enough for going on working.
Then i use my computer...
I like very much Autocad for that kind of vectorial drawings.
That story starts with the dance of 10 pentagons.
Now we can symmetrize.
After that is to draw the 10-pointed star on the corners.
The question is : how to choice the width of the petals (or branch, or rays if you prefer to say) ?
i like the flowered stars
Here is the river. Yes, i have taken some liberties with geometry. I can't denie. I confess. The worse is that i don't feel guilty for that !
I like rivers running in the starry gardens
Now changing the color of the background...
... and get the star nicely dressed with white interlaces.
(i do not use the maximal width )
(here is no more symmetry axe, but a center of rotation)
The traditional pattern is hidden under the flap.
Technic : mosaic of leather incrusted.
On the top is the text section, with some explanations.
The plates are under :
10 colored plates and 190 drawings.