This article explores the spatial distribution of urban settlements in the context of sciences of complexity. Specifically, it tries to explain why urban settlement patterns follow the Power Law. According to the Power Law, an object with the scale of S should occur in a frequency proportional to S-a Besides, this relation is often observed in a self-organizing system. In our earlier research (Yu & Lai, 2001), we conducted computer simulations of self-organizing urban systems based on the principle of increasing returns and the assumption of a uniform plane. We found that urban settlement patterns fit the Power Law. In this research, we relaxed the assumptions of our previous model and expanded our analysis to account for different increasing return functions varying according to scale. According to our simulations, urban systems generated from a random growth model subject to increasing returns usually fit the Power Law regardless of the varied attraction coefficient function. Besides, the rank-size rule is only a special case of the Power Law. Hence, although the rank-size rule is widely accepted and applied by researchers around the world, its occurrence is not unconditional. Finally, we compared the results obtained from different functional forms and concluded that the outcome of the function with “first stationary and then decreasing” returns might be closest to the real-world urban growth experiences.