聚落體系形成之電腦模擬實驗——以報酬遞增觀點為基礎之探討

Computer Experiments on Formation of Settlement Systems: An Exploration Based on Increasing Returns

本文是探討都市聚落體系何以會形成冪次現象（Power law），並嘗試以電腦模擬實驗來驗證報酬遞增是否為構成冪次現象的機制。所謂的冪次法則是指事物出現的規模與頻率間的關係：物體的規模S和其出現次數，呈S-a的比例關係，亦即規模大的事物出現的頻率低，而規模小的事物出現的頻率高，而形成一個自成組織的體系。在都市體系中亦被觀察到有此現象存在，1949年Zipf 提出的等級大小法則（Rank-Size rule），證實冪次現象亦可適用於都市體系。在複雜科學（Sciences of Complexity）中提到，許多自然界與社會科學中的複雜系統，都具有自我組織（selforganization）的特質，冪次法則就是系統具有自我組織性質的證據之一。過去的文獻對於冪次法則形成的機制並未有完整的解釋，由於都市亦為一複雜系統，本研究嘗試由複雜理論中「報酬遞增」的觀念來探討冪次現象的成因，設計電腦程式來觀察報酬遞增與冪次現象之關係。由電腦模擬顯示，依照報酬遞增法則形成的都市聚落，與冪次現象呈高度相關。因此吾人猜測報酬遞增極可能是形成冪次現象的機制之一。 The paper studies why urban systems can be characterized by a power law, and attempts to prove, through computer experiments, if increasing- returns are the underlying mechanisms giving rise to power laws. The so-called 'power law' is referred to as the relationship between the scale and frequency of objects. That is, the number of objects whose sizes exceed S is proportional to S-a. The lager the scale, the lower the frequency; while the smaller the scale, the higher the frequency, and then the system forms an organization automatically. The phenomenon has also been observed in urban systems, the Ranksize rule that Zipf presented in 1949 proving that the power law could also be applied to urban systems. It is specified in the sciences of complexity that many complex systems in natural and social sciences have the characteristics of self-organization, and the power law is one of the evidences that systems exhibit the characteristics of self-organization. Previous related work does not have a complete explanation about how the power law forms. Viewing the city as a complex system, the research tries to investigate the reasons why the power law emerges from the increasing-returns concept in complexity theory, and designs computer programs to observe the relationship between increasing-returns and the power law. The results of the computer experiments show that there exists close relationship between the urban systems that are formed under the increasing-returns assumption and the emergent power law phenomenon. We argue that increasing-returns would be one of the underlying mechanisms through which the power law relationship emerges.