Cycloid with Rolling Construction

The cycloid is defined by these equations:
    c(t) = [t + L*cos(t), L*sin(t)]
The point where the wheel touches the street is momentarily at rest. The connection to the curve point is a generalized radius and the curve tangent is orthogonal to this radius. This is the same for all rolling constructions. See for example Epi- and Hypocycloids
The demo shows at each moment two consecutive positions of the dots. Therefore the image does not look random but suggests a "rotation pattern" of the dot velocities.