4D Sphere Tracer

Using a sphere tracer, 4 dimensional spheres are rendered. The rays start with x y velocities derived from the pixel position, a constant z velocity (depth), and zero w velocity (forth dimension). Each sphere has a gravitational field, the first sphere has a small offset in the forth dimension, thus deflecting rays into the forth dimension. Also note that the reflections on the spheres become invisible when the w coordinate has an offset, because the 4d surface normal now reflects the light not only in 3d space, but also into the forth dimension, so it does not hit any sphere. The small sphere and the sphere on the left rotate around the z (depth) axis. All other "movements" are due to gravitational lensing and/or moving the camera along the 4th dimension. Spheres are colored by the length of xyz-coordinates of the normal (into rgb) and lighted by a directional light source (direction has w=0).