Knot manipulation

Dynamic Manipulation

Any knot or link can be relaxed using a variety of dynamical models. The picture shows the forces acting on a trefoil created from the Conway notation. This allows the knot to go from this

to this

automatically (MPEG animation 50 kbytes, see the knot theory page for more animations).

The dynamical model used most frequently consists of two components:

An attractive force applied to adjacent "beads" on the knot. The beads are the yellow spheres in the above picture. This makes each of blue cylinders act something like a spring.
A repulsive "electrical field" acting between all other pairs of beads.

In most situations, these two forces eventually balance out and something approaching the canonical shape of the knot results.

Go to the KnotPlot Site or Rob Scharein's main WWW page.