Knot Diagram Explorer (2D)

This 2D simulator draws real closed space curves — a trefoil knot and a figure-eight knot, each from its own parametric formula — as flat knot diagrams, breaking the strand that passes farther from the viewer at every self-crossing so the over/under structure reads correctly. Rotating the projection changes how many crossings the flattened drawing shows, sometimes many more than the minimum, which is exactly the point: the crossing number is defined as the smallest count achievable over every possible projection, so it stays fixed at 3 for the trefoil and 4 for the figure-eight no matter how the curve is turned, while the crossings actually visible on screen keep shifting with the rotation slider.