ABSTRACT
There is a close relationship between the hierarchical structure of central place systems with geometrical self-similarity and fractal theory. The theory of fractal geometry pioneered by Mandelbrot has penetrated various fields to describe irregular and complicated shapes, such as coastlines, mountains and rivers. The remarkable features of such shapes are that they are nowhere differentiable and that they possess the property of self-similarity. Arlinghaus has suggested an application of the theory of fractals to the hierarchical structures of central place systems systems which share this geometrical property of self-similarity. She proposes a method for constructing Christallerian central place systems of any K-value, where the K-value is the so-called Lschian number derived from K-value generating function, and for obtaining the fractal dimension of each central place system. Her method appears to create new difficulties, particularly in the procedure for generating the hierarchical structures of K-value central place systems through fractal iteration sequences and in the derivation of the associated fractal dimensions.
