The Wild Knot Page

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To interact with a 3D model below, click on the play button.

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.

All geometry was created in Mathematica.

Trefoil knot

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

Trefoil by brainjam on Sketchfab

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.

Beads by brainjam on Sketchfab

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.

Knot3 by brainjam on Sketchfab