  We define and study the 3-dimensional windings along Brownian paths in the
quaternionic Euclidean, projective and hyperbolic spaces. In particular, the
asymptotic laws of these windings are shown to be Gaussian for the flat and
spherical geometries while the hyperbolic winding exhibits a different long
time-behavior. The corresponding asymptotic law seems to be new and is related
to the Cauchy relativistic distribution.
