This knot employs a hexagon as the starting curve, with three smaller hexagons embedded within it. The scaling factor from the large to smaller hexagons is 1/3. The strands were given arrow-like shapes in order to create a whimsical design that seems to possess a lot of energy. The starting knot has 15 crossings, and the first two iterations have 30 and 75 crossings. The increase in the number of crossings with each successive iteration is 15, 45, 135, ...

The starting knot and its relationship to the hexagons is shown at left, with the first iteration at right:

After two iterations:

All images copyright Robert Fathauer

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