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.

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