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Strong relationships among dimensionless properties of braided streams indicate that similarity is preserved in streams with the same average number of channels but of different sizes. The degree of braiding in streams, conveniently measured by the average number of channels bisected by lines crossing the channel, increases with the product of discharge and gradient, but decreases with higher variance in discharge. A random walk simulation model of braiding duplicates many of the numerical relationships observed in natural streams, suggesting that most of the downstream variation in the number of channels in braided streams is explainable by local fluctuations in discharge and sediment in transport, as opposed to large-scale factors such as valley constriction.