Fractal and Automated Line Generalization

Abstract

The preservation of fractal dimension is proposed as a guiding standard for the automated generalization of statistically self-similar geographical lines. Testings on two different types of such lines show that none of the current generalization algorithms most frequently cited in the literature preserves fractal dimension and statistical self-similarity in a consistent fashion. The walking algorithm used to measure fractal dimension is suggested as an alternative method for generalization. The method not only preserves fractal dimension, it also produces generalized lines whose average angularity and overall displacement are very much in line with the best results provided by other generalization algorithms.

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