Fathauer Kites

Topic:
Kite
In Robert Fathauer's excellent book Tessellations, https://www.mathartfun.com/TessBooks.html, he covers kite spirals, which is a special case of my favorite symmetry of similar quadrilaterals. Daniel Mentrard recently shared his excellent technique for coloring series... so here you go! Raised the question for me: which kites have perfect filling the plane spirals? I left the tools on so you can measure, poke around and investigate.