These examples require a Java-enabled browser, but most modern browsers satisfy that requirement. Move the mouse pointer over each picture to start the animation. Press the HOME key to reset the image. You can click and drag the 3D images to rotate them.

The circle f(t)=< cos(t), sin(t) >, 0 ≤ t ≤ 2 π.
(Repeating in an endless loop.) | |

The path f(t)=< cos(5t), sin(3t) >, 0 ≤ t ≤ 2 π.
(Repeating in an endless loop.) | |

The path f(t)=< cos(t), sin.
^{3}(t) >, 0 ≤ t ≤ 2 π(Repeating in an endless loop.) | |

A parametrized trefoil (overhand) knot, thickened and colored to help you see how it wraps around.
(Repeating in an endless loop.) | |

A more complicated paramtrized knot for your viewing pleasure. The velocity vector has been shortened by a factor of 5.
(Repeating in an endless loop.) | |

The third example in a running theme... The velocity vector has been shortened by a factor of 5.
(Repeating in an endless loop.) | |

The "tornado" f(t)=< t cos(10πt), t sin(10πt), t >, 0 ≤ t ≤ 1. The velocity vector has been shortened by a factor of 5.
(Repeating in an endless loop.) |