Abstract：Fractals of city-size distribution were studied, and the related mathematical models were compared with one another, revised, and synthesized into the general fractal model on rank-size rule:P(k)=A(K-a)-q.The fractal dimensions of size distributions of cities were compared with the β-exponent of 1/fU noise in nature and the 1/r-distribution of city-sizes (Zipf dimension q=1) was presented as the optimumized distribution.It was demonstrated that fractals are essentially orders of hierarchical sturcture of urban systems and D=1/q=1 is the optimum dimension of city-size distributions.
