Japanese Sun Pattern
I want to draw a pattern as above with the circles overlapping. I have the diameter of the outer concentric circle. I want each sun pattern I draw to be equal in size - i.e. equal arc length for the outermost circle (white). Given a distance between each circles center both horizontally and vertically, how would I calculate the chord length to ensure I draw each arc equally (I am drawing on graph paper).
If you want the nested arcs to be concentric, you can choose centers so that they form a triangular lattice:
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Then the arc length is $\frac{1}{3}$ of the full circle, which is simply $\frac{2\pi}{3} r$ where $r$ is the radius of the outermost circular arc. The following is an example created by this pattern:
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Remark. If you look closely at your pattern, nested arcs actually do not seem concentric. If you allow such feature, then there is an huge degree of freedom of mimicking them.
p.s. The Mathematica 11 code I used to create the image: