  It is well known that conventional simulation algorithms are inefficient for
the statistical description of macroscopic systems exactly at the critical
point due to the divergence of the corresponding relaxation time (critical
slowing down). On the other hand the dynamics in the order parameter space is
simplified significantly in this case due to the onset of self-similarity in
the associated fluctuation patterns. As a consequence the effective action at
the critical point obtains a very simple form. In the present work we show that
this simplified action can be used in order to simulate efficiently the
statistical properties of a macroscopic system exactly at the critical point.
Using the proposed algorithm we generate an ensemble of configurations
resembling the characteristic fractal geometry of the critical system related
to the self-similar order parameter fluctuations. As an example we simulate the
one-component real scalar field theory at the transition point $T=T_c$ as a
representative system belonging to the $3-D$ Ising universality class.
