  We consider the set of monofractals within a multifractal related to the
phase space being the support of a generalized thermostatistics. The
statistical weight exponent $\tau(q)$ is shown to can be modeled by the
hyperbolic tangent deformed in accordance with both Tsallis and Kaniadakis
exponentials whose using allows one to describe explicitly arbitrary
multifractal phase space. The spectrum function $f(d)$, determining the
specific number of monofractals with reduced dimension $d$, is proved to
increases monotonically from minimum value $f=-1$ at $d=0$ to maximum $f=1$ at
$d=1$. The number of monofractals is shown to increase with growth of the phase
space volume at small dimensions $d$ and falls down in the limit $d\to 1$.
