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With my limited knowledge, the only way I could figure out how to make it work, and work well without giant seams in the joinery, would be to make the beginning of two chessboards. Which would be gluing alternating strips of light and dark wood together. Now when I did my chessboard, I then crosscut that giant glued up panel of 8 strips 8 more times, and flipped every other crosscut stripe to get the checkerboard pattern.
With this, I'd have to either use a bandsaw and cut those curves very, very carefully, or use a router with a straight bit and a nail in the middle to then make perfect circles. There would be a lot of waste, but between the two boards of stripes I began with, the remainder should complement the circles I routed out of the other.
I don't think I could use just one, because no matter what the kerf of the blade would make a giant seam if I just tried to rotate the two pieces and glue them back together. You can sort of get away with it maybe on shallower curves. Maybe use some sawdust and glue to try to fill anywhere that looks too bad. But the sharper curves towards the center would absolutely show the width of the blade kerf if you tried to use a single boards worth of material.
I'd expect a lot of that chessboard depends on how heavily you're committed to the bit. If it just needs to look right from the top but you want the grain patterns to look intact, that's a great place to rent some time on a cnc to make an inlay or even just use a bunch of veneer or burl and a sharp exacto knife. Would still require a lot of chisel or marking knife work to get those precise corner angles, but it'd save you a ton of material and a lot of really finicky jigsaw work or sanding.
Every time I see someone bust out a CNC machine, I get sad. I can certainly see their utility if it's your business. Not using one basically seems like you are leaving money/productivity on the table. But currently I'm enamored with the craftsmanship of woodworking. Getting my tools perfectly square and flat. Really nailing some perfect miter joints. Things like that.
That's fair; there's certainly a lot more romance and skill to hand tools or conventional power tools, and seeing a full CNC machine used for glorified bowl or crosscut work gets me a little disappointed myself. And it's definitely the sort of tradework that you have to love the process of doing it to really get the most out of a piece, and it's hard to do that when it's all gcode.
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