Zipf’s Law and the Spatial Interaction Models

Abstract

本文的主要目的是以模擬方式分析最大熵概念為基礎所推導的都市交互與成長過程，是否會衍化出趨近普瑞夫定理(Zipf`s Law)的城市分配。模擬結果顯示：(一)動態交互模型在不同的參數值下可產生穩定或不穩定的成長型式。(二)在穩定的衍化過程中，本文的模型可產生決定性的與隨機的成長過程。(三)決定性的與隨機的成長型式都會趨近於普瑞夫定理的分配型態。

It is well known that the size distribution of cities is surprisingly welldescribed by Zipf`s law. It is considered the criterion for the local growthmodel. The purpose of this paper is to explain Zipf`s law through the use ofa dynamic process based on a spatial interaction model derived from entropy. Empirical findings show that: (1) the purposed dynamic process can generateboth stable and unstable patterns in accordance with the value of theparameters (2) in the stable evolution the model can generate bothdeterministic and stochastic growth processes (3) both deterministic andstochastic growth processes converge in Zipf`s pattern and (4) evidence fromcities in Taiwan shows a diminishing estimated intercept and slope as theproposed model predicted. Size distribution in Taiwan converges to Zipf`spattern.