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The performance of electrochemical devices like fuel cells is strongly affected by the transport of electrons between interconnects and active regions of an electrode. We examine the use of an auxiliary, precious metal current distributor placed over the cathode of a solid oxide fuel cell to supplement the transport process. Cell resistance was minimized by computer modeling as a function of the shape of the structure under the constraint that its total volume is fixed. The optimal shapes are shown to be fractals that resemble structures found in nature. A thin fractal current distribution structure made from platinum was demonstrated to facilitate the transport process in oxygen pump cells constructed from porous lanthanum strontium manganite (LSM) - yttria-stabilized zirconia (YSZ) composite electrodes on a 15 µm thick tape of 3 mol percent YSZ.