Rudin-Shapiro Curve

The Rudin-Shapiro sequence gives the parity of the number of (possibly overlapping) 11 blocks in the binary representation of . A curve can be derived from this sequence as follows. At step , if is even, turn right 90°; otherwise turn left 90°. The curve visits every lattice point in one eighth of the plane precisely twice. (Here the corners are rounded for clarity.)

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