In the process of a fluvial evolution, the water discharge, sediment charge and stream energy expenditure dominant the channel patterns of a river. Given water and sediment, an alluvial channel is self-organizing, adjust to achieve a stable equilibrium state, and form a characteristic channel geometry (channel width, depth and slope). In the equilibrium condition which is also said to be in regime or graded, the flux of the water and sediment from the watershed should be equal to the flux of the downstream channel(s). By studying bed load transportation and stream power conversion on a steady and uniform stream, we suggest two characteristic parameters that are energy conversion length and regime transportation length of sediment. The regime equation and equations of fractal features are set here. All cross-section variables (stream width, depth and velocity) of a regime stream, who theoretically derived under the equilibrium of sediment transportation and the conversion of stream power, are exclusively determined by the two lengths and the water discharge.