关键词: 异速标度, 城市化, 城市形态, 城市体系, 分形, 自组织网络

Abstract: The allometric scaling analysis in urban studies originated from biology and general system theory.At first,it was employed to analyze the allometric relation between urban and rural population associated with urbanization.Before long,the studies on the scaling relation between urban area and population became the mainstream of the allometric analysis.The chief aim is to reveal the relationship between size and shape of cities.But a dimension conundrum arose.Urban area can be regarded as a 2-D measurement,and urban population used to be treated as a 3-D measurement.Thus,according to the principle of dimensional consistency,the scaling exponent of urban area and population should be 2/3. However,it does not conform to reality.Then,urban population was treated as a 2-D measurement.If this was true,the allometric scaling exponent should equal 1.However,this does not yet tally with the actual situation.Geographers and city scientists were placed in a dilemma whether to treat urban population size as a 2-D or a 3-D measurement because the observed scaling exponent values always come between 2/3 and 1.The geographical students failed to extricate themselves from the theoretical predicament before the introduction of the concept of fractional dimension.The rapid rise of fractal geometry and complexity theory results in the rejuvenation of alloemetric analysis of cities associated with scaling law.Now, allometry has been applied to urban form,urban ecology,urbanism,urban dynamics,and urban systems.All of the applications are the bases of studies on urbanization.One of the most significant research directions of allometry in urban studies in future may be the allometric scaling analysis in urbanization.

Key words: allometric growth, allometric scaling, fractals, urban evolution, urban form, urbanization, self-organized network