環顧過去一系列關於都市供給網絡的異速增長規律 (allometric scaling law) 的研究，其最大貢獻在於重複地確認一個跨越不同住居歷史條件、不同自然地理 環境與不同經濟發展水準的數學通用模式，來客觀地檢測與定量地預期個別國家 或個別區域內的都市發展與都市增長究竟「會如何」或「將如何」改變都市之實 質環境。但過去文獻卻忽略了異速增長規律應用於都市發展過程時所可能蘊藏的 變化和軌跡，從而缺乏對於都市供給次系統的異速增長指數 (allometric exponent) 在連續時刻點之動態探查。除此之外，既有文獻亦未曾考慮眾多系統相關的都市 個體，與都市個體所共同突現的異速增長指數之間的同步變化程度或主次關係， 以致目前仍無法進一步認識眾多系統相關的都市個體，在有機的和有組織的異速 增長過程裡所潛藏的關聯性和基本機理，並因此缺乏相對應的都市個體層次的規 劃啟示與指導意涵。
研究擬根據臺灣地區自1991 年至2010 年之既有統計數據集 (Urban and Regional Development Statistics)，藉由異速增長規律的對數線性形式執行數據擬 合與檢測，並結合灰色關聯分析之序列比較結果，試圖彌補這些在過去文獻所未 曾深入的研究議題。研究結果發現：(一) 臺灣眾多都市個體的人口規模與其廣 泛類別的供給變量，確實可在保有良好的擬合配適度的前提下，共同突現出可類 比生物物種的與自相似的異速增長關係；(二) 當臺灣的都市個體的人口規模改 變， 則其所伴隨的廣泛類別的供給變量， 幾乎皆是非線性的異速增長 (allometry)，而非傳統規劃或實務操作所預設的和認知的線性增長；(三) 本研究 內容所掌握的和檢測的各種都市供給變量，其異速增長指數普遍隨時間推進而波 動，並非如同生物節奏般地亙古不變，當然亦不存在固定的異速增長指數 (如 Kleiber’s Law)；(四) 臺灣都市個體的人口規模大小，以及臺灣都市個體對於集 體層次的都市供給網絡的異速增長規律的關聯強弱，兩者之間並沒有必然關係； (五) 臺灣都市個體的政治經濟分量，以及臺灣都市個體對於集體層次的都市供 給網絡的異速增長規律的關聯程度，兩者之間卻極可能關係非常緊密。

The past series of studies on allometric growth law for urban supply networks verifies and confirms a common mathematical model across different historical, geographical and socio-economic conditions. However, the previous literature has disregarded the trajectory of allometric exponents in the evolution of cities, and has neither provided dynamic descriptions nor explored trends over time. Furthermore, the literature has not measured or clarified effect of interactions among individual cities in a network with the collective growth phenomenon in common interaction of maintaining networks. Therefore, planners are still unable to exploit the potential mechanisms or underlying generic principles of individual cities in organic and allometric process to improve human settlements, urban environment and city design.This study investigates and verifies existing statistical data (Urban and Regional Development Statistics) in Taiwan from 1991 to 2010 based on log-linear forms of allometric growth and grey incidence analysis (grey sequences), to bridge the gap of knowledge in the past literature. This finding indicates the following conclusions: (1) that an allometric scaling law of self-organization and self-similarity of individual cities is emerging in Taiwan; (2) that the allometric exponents of various supply systems change over time, unlike immutable biological rhythms; (3) that the urban supply systems show non-linear allometric growth, rather than linear as in traditional planning practice; (4) that the population scale of a city does not affect allometric scaling law of urban supply networks, (5) and a close relationship exists between political or economic status of individual cities and influence of individual cities affecting the allometric scaling law of urban supply networks.