Transmission electron micrographs of thin evaporated gold films were analyzed by computer. For length scales above 10 nm, the irregular connected clusters show a perimeter linearly proportional to area. Near the percolation threshold the large-scale power-law correlations and area distributions are consistent with the scaling theory of second-order phase transitions. Geometrically, the boundary of all clusters is a fractal of dimension $D=2\mathrm{}$ while individual boundaries are of fractal dimension $D_C\approx 1.9$.

• Received 30 June 1982

DOI:https://doi.org/10.1103/PhysRevLett.49.1441