Inspired by this Veritasium Youtube video.
Consider a kite and dart style penrose tiling Kites And Darts. The goal is to color the kites and darts such that no two adjacent pieces (touching edges) are the same color.
I have 2 main inquiries. First, I have made an assumption that a minimum of 5 different colors are required to color an infinite plane of kites and darts since each piece has 4 edges. Is there any reason that 5 colors would fail at some point? What if, additionally, two pieces cannot be the same color if they touch at a corner?
Secondly, is there some process one can follow, either while constructing the pattern, or while coloring it afterword, that would ensure you can color out to infinity without mistakes?
Thank you for taking the time to read my question! Apricot Jam