This knot employs an octagon as the starting curve, with four smaller octagons embedded within it. The octagons are semi-regular, with long edges the square root of two times the short edges in length. The scaling factor from the large to smaller octagons is 1/3. The starting knot has 9 crossings, and the knot has 57 crossings after one iteration.
The starting knot and its relationship to the octagons is shown at left, with a more stylized version of the starting knot at center, and the first iteration at right:
After two iterations:
After two iterations, with two colors to better illustrate the path of the strand:
All images copyright Robert Fathauer
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