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