Animation of two cars (blue and red dots) racing along a track.

Although the cars move at the same speed, they seem to pull ahead and fall behind at various points during each circuit. This happens because the car taking an inside curve has a temporary advantage over the car taking an outside curve. But in any closed loop, however complex, these factors will balance out causing both cars to cross the finish line at the same time.

The animation is augmented by some novel visualizations which show what portions of the track give an advantage to the red car, and what portions benefit the blue car. The histogram shows the magnitude of that advantage at each point. The arrows show the changing direction of each car.

The network builds the track out of arcs and sine waves and uses my trace node to derive separate paths for the two lanes. In addition to the network and screenshot, I have also attached a movie of the race.

Enjoy!

John