The Wild Knot Page


All geometry was created in Mathematica.

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To interact with a model, place the mouse pointer over it. Dragging will rotate the model, Shift-vertical-drag will zoom it. Releasing the mouse while dragging will make the model spin. For more instructions, consult the LiveGraphics3D page .

This work is based on a construction suggested by B. Maskit in his text Kleinian Groups. A set of spheres is arranged, like a set of beads, along the curve of a trefoil knot. The set of inversions in these spheres generates a group whose limit set is a wild knot.

Trefoil knot

To the right is an interactive model of a trefoil knot.

Spheres arranged in a trefoil knot

To the right is an interactive model of a set of spheres that has been arranged along a trefoil knot. Each sphere is in tangential contact with its two neighbours, but is a non-zero distance from all the other spheres.

Level 3 knot

To the right is an interactive model of an approximation to the limit set of the group generated by inversions in the spheres shown above.