The reason it's showing those interesting paths is because it's plotting the relative motion of the planets with respect to the Earth.
So visualize the moving Earth in the center of each image with the other respective planet moving relative to the Earth. Since both are moving and rotating about the Sun we get these interesting motions with a lot of structure.
This is the theory of epicycles which was the main theory of the motion of the planets before the heliocentric view became prominent.
Cruithne orbits the sun at about the same distance as the Earth, and so with about the same period as the Earth. The orbit varies, so sometimes it's closer to the sun than we are, and sometimes further from it. So, seen from the Earth, what it's doing is moving around us - sometimes ahead of us in orbit, sometimes sunward, sometimes behind us, sometimes starward. But its orbit isn't pefectly elliptical, and it has more inclination, so it traces out an interesting path.
That video is a recycling of an older video which had a very informative voice-over, rather than some cheesy music. That video doesn't seem to be online any more, sadly.
Cruithne's orbit was only figured out in 1997, and i remember that it was briefly very cool (for small values of cool). Stephen Baxter, who was a top science fiction writer at the time, featured it in his novel 'Time'.
Steven Fry in an episode of his funny informative show QI incorrectly called Cruithne Earth's second moon. It's not; it orbits the sun, not the Earth. I don't think it's ever directly sunward or starward from us, but always either in front of us, behind us, or on the other side of the sun.
From the article:
"From left to right, these rosettes show the surprisingly beautiful paths of Mercury, Venus, Mars, Jupiter, Saturn, and Uranus as seen from Earth. "
Before we understood that the planets orbit the sun (more or less), astronomers thought they orbited the earth, and tried to explain these paths using epicycles - note the diagram halfway down:
A really impressive use of Python for visual graphics design! I wonder what kind of packages you'd need to reduce the amount of work done in external editors, probably something that can make SVG.
Both the "Greek camp" (L4) and the "Trojan camp" (L5) of asteroids in resonance with Jupiter are called "Trojan Asteroids" - the group is named after the Trojan War, not Trojans as a people.
If you look carefully at the orbit of Mercury you can see that it is elliptical. Pluto is also somewhat elliptical, which is hard to tell directly but given away by the fact that it crosses inside the Neptune orbit (this is also mentioned in the text). If you compare the distance between Earth and Mars around the "AST" in "Mars Crossing Asteroids" and around "Fortuna" you can see that the Mars orbit is somewhat elliptical. All the other planets orbits are much closer to circular and you can not see the eccentricity by eye.
Just to add the data, Mercury with 0.206 and Pluto with 0.248 are the only ones with a clearly visible eccentricity, the rest of the planets have eccentricity <0.1. For instance our Earth has 0.017 eccentricity, with an perihelion of 0.98 AU and an aphelion of 1.02 AU, so quite difficult to tell visually.
