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This work develops a preliminary method for coding random self-similar patterns as a series of numbers and investigates the corresponding algorithm to calculate the topological distance between starting point and the link in the generated fractal pattern from the code series. With reference to the wide range of stochastic property in natural patterns, a process for generating fractal patterns with various generating probabilities of the pattern links denoted as separately random self-similar generation or separately random fractal is proposed. To assess the adaptability of the process, the coding method is applied to the generation of a random self-similar river network and the corresponding algorithm for calculating topological distance of the links is used to determine the width function of the pattern. The width function-based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results show that the separately random self-similar generating algorithm can be implemented successfully to calculate hydrologic responses.

An approach to apply the fractal concept to estimate hydrologic response is proposed in this paper by matching suitable self-similar networks (SSNs) to a specific watershed, and modeling the runoff with a width-function based geomorphologic instantaneous unit hydrograph (WF-GIUH). In order to work out the identification between a specific basin and SSNs that are generated by an interior generator cooperating with an exterior generator, a generalized width function is derived. Subsequently, cumulative width functions on the basis of the derived function, as well as the informational entropies are used as criteria to decide the best patterns of the two cooperating generators for the specific watershed. The WF-GIUH model is then applied to calculate the runoff of this watershed as an outcome of the estimation. To assess the adaptability of the estimation model, San-Hsia watershed of Northern Taiwan is selected as a study area, where the analytical results of the outflow estimation indicate that the fractal algorithm has been implemented successfully for the calculation of hydrologic responses.