  Motivated by the well-known fractal packing of chromatin, we study the
Rouse-type dynamics of elastic fractal networks with embedded, stochastically
driven, active force monopoles and force dipoles that are temporally
correlated. We compute, analytically -- using a general theoretical framework
-- and via Langevin dynamics simulations, the mean square displacement (MSD) of
a network bead. Following a short-time superdiffusive behavior, force monopoles
yield anomalous subdiffusion with an exponent identical to that of the thermal
system. In contrast, force dipoles do not induce subdiffusion, and the early
superdiffusive MSD crosses over to a relatively small, system-size-independent
saturation value. In addition, we find that force dipoles may lead to
``crawling" rotational motion of the whole network, reminiscent of that found
for triangular micro-swimmers and consistent with general theories of the
rotation of deformable bodies. Moreover, force dipoles lead to network collapse
beyond a critical force strength, which persists with increasing system size,
signifying a true first-order dynamical phase transition. We apply our results
to the motion of chromosomal loci in bacteria and yeast cells' chromatin, where
anomalous sub-diffusion, MSD$\sim t^{\nu}$ with $\nu\simeq 0.4$, were found in
both normal and ATP-depleted cells, albeit with different apparent diffusion
coefficients. We show that the combination of thermal, monopolar, and dipolar
forces in chromatin is typically dominated by the active monopolar and thermal
forces, explaining the observed normal cells vs the ATP-depleted cells
behavior.
