Figures for "Cantor knots"

Cameron Browne
Dec 2004

Figure 1. A knot in the Celtic style and its double-interlaced counterpart.

Figure 2. The Cantor set and a Cantor braid.

Figure 3. A loop with a 1/3 incision stretched around to cut it into two loops.

Figure 4. More complex incision patterns.

Figure 5. A trivial knot, a Cantor knot with a single woven level 1 incision, and a Cantor knot with multiply woven level 2 incisions.

Figure 6. Split weave rule: a bad weave (left) and an acceptable weave (right).

Figure 7. Higher levels of recursion do not necessarily provide a more interesting weave.

Figure 8. An embellished knot woven at levels 0, 1 and 2, with source knot (inset).

Figure 9. An embellished knot woven at level 3, with source knot (inset).