Background

A fractal is an object that exhibits self-similarity on different scales. Mathematical fractals have an infinite level of detail and are generated by iterative processes.

A knot is a closed curve in space that does not intersect itself anywhere. A 2-D drawing of a knot is a projection of a 3-D knot. Knots are classified according to their minimum number of crossings. Distinct knots can't be rearranged to form one another.

There have been very few attempts to combine fractals and knots. Carlo Séquin showed a couple of examples in Boulder in 2005, and Paul Gailiunas showed another example at Bridges in 2006.

Iterated knots are obtained by applying the same type of crossings iteratively. To be considered knots, they must be unicursal. In the limit of an infinite number of iterations, they become fractal knots. Fractal knots are wild; i.e., they have an infinite number of crossings.