城市体系规模结构预测方法应用研究——以内江市为例

本文利用城市体系规模分布模型对内江市城市体系分形特征及规模结构进行了分析预测,指出了内江城市体系发展规律及促进其快速发展规律及促进其快速发展的对策措施。     

城市规模分布的分形和分维

研究城市规模分布的分形特征,修正了一些位序—规模模型,将历史上出现的有关城市规模分布的模型统一在分形形式之下,并给出了具有一般意义的三参数Ｚｉｐｆ模型：Ｐ（ｋ）＝Ａ（Ｋ－ａ）－ｑ。将Ｚｉｐｆ维数与大自然１／ｆβ起伏的β指数进行类比,认为分维Ｄ＝１／ｑ＝１是一种先验的优化维数,进而提出结构优化的１／ｒ型城市位序—规模分布,以此作为城市体系等级结构规划的依据之一。     

The fractal geometry of ancient Maya settlement

Ancient Maya settlement patterns exhibit fractal geometry both within communities and across regions. Fractals are self-similar sets of fractional dimension. In this paper, we show how Maya settlement patterns are logically and statistically self-similar. We demonstrate how to measure the fractal dimensions (or Hausdorff–Besicovitch dimensions) of several data sets. We describe nonlinear dynamical processes, such as chaotic and self-organized critical systems, that generate fractal patterns. As an illustration, we show that the fractal dimensions calculated for some Maya settlement patterns are similar to those produced by warfare, supporting recent claims that warfare is a significant factor in Maya settlement patterning.     

论分形与旅游景观

本文运用分形理论论述了旅游景观构成要素的自相似性质,指出人类旅游行为本质上是为了摄取地理信息,而分形体是有效的信息之源,能使游人产生负熵的感受(即美感)。历史的混沌过程与地貌的分形构造形成了非富的旅游资源。借助分形学原理,依据有序与无序对立统一的原则设计旅游景观,必将使旅游资源得以合理地开发和充分地利用。     

中心地体系中的分形和分维

中心地体系中蕴含着分形结构,具有多分维特征。本文借助koch雪花和随机Sierpinski图形揭示了中心地k=3体系和k=4体系的生成机制,提出了城乡聚落体系和城市-交通网络的两种分形模型,这些模型的分维与S.Arlinghaus的发现具有对应性。     

Microseismic Signal Spectra,Energy Characteristics,and Fractal Features Prior to Rock Burst: A Case Study from the Qianqiu Coal Mine,China

Microseismic (MS) technology has been widely adopted for monitoring coal and rock dynamic disasters. Insights into MS wave characteristics contribute to the accurate prediction of these disasters. In this study, MS wave characteristics were analysed from three aspects: the signal spectra, wavelet packet energy and fractal features. It is shown that prior to the rock burst, the MS wave main frequency decreased following a power law, the amplitude linearly increased, the wavelet packet energy tended to become concentrated on the low frequency bands, and the correlation dimension decreased. When the rock burst occurred, the MS wave main frequency, wavelet packet energy and correlation dimension declined to their lowest levels. Meanwhile, the amplitude rose to a maximum. Therefore, the MS wave characteristics in this study were found to effectively identify and extract precursor information of value for predicting rock dynamic disasters.     

圆形城市商品销售的空间受限模型

本文首先提出商品价格空间分布的分形函数,以此为基础导出商品销售的空间受限模型,该模型揭示了人地非线性相关的某些机制,并为企业选择投资区位提供了分析方法。