Ogg Video (try with Google Chrome or Firefox)
The animation on the left shows a 3D random walk originating in the center of a sphere, shown until it first crosses the surface of the sphere. This is called a first passage event. The system is rotated around the x axis to keep the particle in a plane parallel to the screen and going through the center of the sphere. That way it always hits the surface of the sphere at the outer perimeter line, making the first passage event more obvious in the 2D representation.
WebM Video (try with Google Chrome)