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In this paper we are examining diffusion properties of stationarycontinuous-time Weierstrass walk (CTWW). We are showing it is a multi-phaserepresentation of the L\'evy walk. The hierarchical spatial-temporal coupling,combined with coupling between dynamic variables define the CTWW process. Thewalker moves here with a piecewise constant velocity between trajectory turningpoints. We have found the diffusion phase diagram of the CTWW consisting notonly of anomalous non-Gaussian or non-fBm phases but also Brownian yetnon-Gaussian ones. We compare the diffusion phase diagram of the stationaryCTWW with the corresponding hierarchical continuous-time Weierstress flight(CTWF). The instantaneous jumps between trajectory turning points preceded bywaiting define the CTWF process. It is a hierarchical representation of theL\'evy flight. We have found the diffusion phase diagram of the CTWF to be asmall part of the corresponding CTWW one.

Multi-phase long-term autocorrelated diffusion: Stationary continuous-time Weierstrass walk vs. flight