  The concept of z-scaling previously developed for analysis of inclusive
reactions in proton-proton collisions is applied for description of processes
with polarized particles. Hypothesis of self-similarity of the proton spin
structure is discussed. The possibility of extracting information on
spin-dependent fractal dimensions of hadrons and fragmentation process from the
cross sections and asymmetries is justified. The double longitudinal spin
asymmetry A_{LL} of jet and pi0-meson production and the coefficient of
polarization transfer D_{LL} measured in proton-proton collisions at sqrt s =
200 GeV at RHIC are analyzed in the framework of z-scaling. The spin-dependent
fractal dimension of proton is estimated.
