This is the second sheet of patterns in this series. All of these patterns are based upon a 30-60-90deg triangle. These are straight forward patterns and require very little by way of measuring.
The first three patterns are variations on each other. The variations are achieved by changing the starting points and/or the omission of lines. The only other controllable element is the offset of the triple line portions.
The remaining two patterns require the layout of a square grid. The size of the squares in the grid dictates the individual pattern. The direction of the pattern or the omission of lines is what generates the overall pattern.
I think it’s quite remarkable how simply changing the direction can generate a completely different looking pattern. You can also use shading to reveal diamonds, stars and pinwheels as well.
PDF download:
Hillbilly Inlay Pattern Sheet No.2
Greg Merritt
HILLBILLY DAIKU 
Thanks Greg. This is fascinating.
Coincidentally I recently watched a TED talk about math(s) and symmetry. Now, I am no mathematician, but the idea that there is a formal language for symmetry, and the realisation that there is a finite number of possibilities for the rotation of a given pattern was interesting, and perhaps relevant to what you are doing here.
All the best
Paul
Thanks for the link Paul. Very interesting. The more I research the deeper this thing goes. It’s amazing what is possible with a few lines and arcs and I’m just scratching the surface.
Greg
You must be familiar with the artist MC Escher? I have a framed copy of ‘Relativity’ that i used to have hung in my office, was a great piece to point to when i needed reminding myself to consider another persons perspective. http://www.mcescher.com/gallery/back-in-holland/relativity/
Escher is awesome! I’ve been looking at his stuff and geometric optical illusions for some additional inspiration. There are numerous possibilities.
Greg