In this demonstration, the green vehicle wanders through its world, wrapping around the window boundaries. Wandering is a type of random steering which has some long term order: the steering direction on one frame is related to the steering direction on the next frame. This produces more interesting motion than, for example, simply generating a random steering direction each frame.
This steering behavior maintains state, the "wander direction" which is represented here as a red dot. At each time step a random offset is added to the wander direction. The modified wander direction is constrained to lie on the black circle. (For 3d steering the circles are replaced by spheres.) The black circle has unit radius and its center is located sqrt(2) units along the vehicle's forward axis, it is shown enlarged in this diagram. This model of wandering is parameterized in terms of: