  In this paper we are examining diffusion properties of stationary
continuous-time Weierstrass walk (CTWW). We are showing it is a multi-phase
representation of the L\'evy walk. The hierarchical spatial-temporal coupling,
combined with coupling between dynamic variables define the CTWW process. The
walker moves here with a piecewise constant velocity between trajectory turning
points. We have found the diffusion phase diagram of the CTWW consisting not
only of anomalous non-Gaussian or non-fBm phases but also Brownian yet
non-Gaussian ones. We compare the diffusion phase diagram of the stationary
CTWW with the corresponding hierarchical continuous-time Weierstress flight
(CTWF). The instantaneous jumps between trajectory turning points preceded by
waiting define the CTWF process. It is a hierarchical representation of the
L\'evy flight. We have found the diffusion phase diagram of the CTWF to be a
small part of the corresponding CTWW one.
