聚落體系形成之電腦模擬實驗－－不同函數型態下的探討

Computer Experiments on Formation of Settlement Systems: An Exploration Based on Multiple Functional Forms

本文是探討複雜理論對都市聚落體系空間分布之影響，試圖解釋何以都市聚落體系會形成冪次現象（Power law）。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，而形成一個自成組織的體系。在先前的研究中曾指出，根據報酬遞增理論所設計的電腦模擬中，在均質平面平面的假設下，會呈現出高度符合冪次現象的都市體系（于如陵，賴世剛，2001）。本文在此一基礎上，將模型的假設條件放寬，使擴增為不同函數之報酬遞增型態下的探討。本研究基於複雜理論，設計電腦程式來模擬都市聚落體系之形成。本研究顯示，基於隨機成長的都市體系模擬結果，不論所依據的函數型態為何，大多數都高度符合冪次法則。等級大小法則為冪次法則的特例，但符合冪次法則的機制，未必符合等級大小法則。因此雖然等級大小法則已被廣為都市研究者奉為圭臬，在世界各地加以應用，但其成立並非毫無條件。另外本研究認為，「先固定後遞減」可能是最符合真實世界的都市體系成長歷程的推動機制。 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.