The starting curve is a square, and there are two smaller squares enclosed within it, both of which are scaled by 1/3 and neither rotated nor reflected. There are four points on each square at which strands connect, located at midpoints of the edges. The starting knot has 7 crossings, and after one iteration the knot has 17 crossings. The number of crossings for the second through fifth iterations is 37, 77, 157, and 317. Note that the increase in the number of crossings from one iteration to the next is 10, 20, 40, 80, 160, ...

The starting knot and the first two iterations, with the squares shown in dotted lines:

After three iterations:

After three iterations, with two colors to better illustrate the path taken by the strand:

All images copyright Robert Fathauer

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