  Using finite temperature SU(3) lattice gauge theory in the fixed scale
approach we analyze center properties of the local Polyakov loop L(x). We
construct spatial clusters of points x where the phase of L(x) is near the same
center element and study their properties as a function of temperature. We find
that below the deconfinement transition the clusters form objects with a
fractal dimension D < 3. As the temperature is increased, the largest cluster
starts to percolate and its dimensionality approaches D=3. The fractal
structure of the clusters in the transition region may have implications
regarding both the small shear viscosity and the large opacity of the Quark
Gluon Plasma observed in heavy-ion collision experiments.
