This knot possesses seven-fold symmetry. The first example below is not particularly interesting as a fractal, as the number of copies of the original knot remains one at each iteration. However, it makes a compact and graceful figure and is included for that reason. An analogous iterated knot can be constructed for any knot of this type (arranged in a ring, the first knot in the knot table for the given number of crossings) if and only if the number of crossings is a prime number.

The second example below increases the number of copies of the original knot sevenfold at each iteration. This is analogous to the fractal knot shown for knot 5

One possible starting self-similar knot:

After one iteration:

After two iterations:

A second possible starting self-similar knot:

After one iteration:

All images copyright Robert Fathauer

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