Fractal electrode designs are proposed for electrochemical devices. A zeroth-order approximation fractal model is analyzed and basic insights into the scaling laws of the electrical properties and the surface-to-area ratio are derived. Fractal electrodes can minimize internal resistance while maximizing surface-to-volume ratios. Recent carbon microelectromechanical systems ͑C- where V is the variable in question, a is a constant, and b is the scaling exponent. The fascinating empirical observation that has perplexed many scientists and has been a source of much debate has been the fact that the exponents ͑b in Eq. 1͒ of many variables, including cellular metabolism ͑b = −1/4͒, heartbeat ͑b = −1/4͒, maximal population growth ͑b = −1/4͒, life-span ͑b = 1/4͒, blood circulation ͑b = 1/4͒, embryonic growth/development ͑b = 1/4͒, metabolic rates of entire organisms ͑b = 3/4͒, cross-sectional areas of mammalian aortas ͑b = 3/4͒, and cross-sectional areas of tree trunks ͑b = 3/4͒ are multiples of 1/4
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