All geometry was created in Mathematica.
This page will not work unless Java is enabled in your browser. In any case it will take several seconds to load.
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.
To the right is an interactive model of 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.
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.