Move the mouse left or right to accelerate. Click the stage to zero out your relative velocity. The project generates grid lines for space & time contours, and your worldline path is drawn out behind you. This does not take into account time dilation. If it did, you'd leave the gridlines behind much faster when traveling at high zeta!
This is a model of how relative spacetime transforms in a penrose conformal model of space-time. http://en.wikipedia.org/wiki/Penrose_diagram All paths lead to the point at the top, and all 45-degree lines are light-speed paths. Each grid-line, horizontal and vertical, actually represents an equally-spaced interval of distance in space or in time.