This demo includes three windows.

The window "Curve: X(t)" displays the curve X(t).

The window "Perturbed Tangential Image" displays the tangent vector T(t0) and a curve that it traces out. The tangent vector is perturbed slightly (with the magnitude of this perturbation controlled by parameter u) so that the curve that it traces out does not overlap itself.

The rotation index is the total change of direction angle from tmin to tmax divided by 2π, which is visualized in the "Perturbed Tangential Image" window.

You can change t0, u, and X(t) in the control window. The control window also includes a list of curves that you can enter for X(t), and parameters used in defining those curves. For example, enter cardioid(t) in the X(t) textbox to make X(t) a cardioid. Changing k will then change the cardioid.