Named after French mathematician Paul Lévy, the C curve is one of a family of fractal curves, also called dragon curves. It is simply constructed. Start at the origin, facing East. Let 'F' mean move forward one unit, and let 'L' and 'R' mean turn left and right ninety degrees respectively. The first iteration is 'F'. Each subsequent iteration consists of the previous list, then 'L' then the previous list again, then 'R'. So second iteration is 'FLFR', and the third iteration will be 'FLFRLFLFRR'.
The first 14 iterations of the curve are drawn here, using 16383 line segments.