We present the results of measurements of transport properties of 6th order Sierpinski gasket arrays of weak Josephson junctions. The system shows a broad fluctuation-dominated resistive transition. The temperature dependence of the resistance, however, does not fit the existing theory of fluctuation effects for dimension d=l, d=2, or d=1.585, the fractal dimension of the gasket. The current-voltage characteristics exhibit power-law behavior, but with the exponent varying smoothly with temperature, in contrast to those of 2D arrays. The sample voltage as a function of magnetic field reveals dilation invariance as the field axis is expanded by a factor of 4, reflecting the self-similar geometry of the gaskets.