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 51. An analogous iterated knot can be constructed for any knot of this type if and only if the number of crossings is an odd number.


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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