The Fractal Dimensions of Lithic Reduction

The fractal distribution is the best statistical model for the size-frequency distributions that result from some lithic reduction processes. Fractals are a large class of complex, self-similar sets that can be described using power-law relations. Fractal statistical distributions are characterized by an exponent, D, called the fractal dimension. I show how to determine whether the size-frequency distribution of a sample of debitage is fractal by plotting the power-law relation on a log-log graph. I also show how to estimate the fractal dimension for any particular distribution. Using debitage size data from experimental replications of lithic tools, I demonstrate a fundamental relationship between the fractal dimension and stage of reduction. I also present archaeological case studies that illustrate the simplicity and utility of the method.     

城市形态分维测算和分析的若干问题

本文讨论了城市形态分维测算和分形分析的几个常见问题,这些问题常使初学者感到困惑。主要论述如下内容:分维的性质、特征和基本含义,无标度区的城市地理学意义、判断和界定方法以及城市演化分析中的作用,城市形态分维分析的一般步骤,分维与其他参量的关系,等等。作者强调,要想避免研究中出现的伪分形现象导致的错误结论,必须有效利用双对数坐标图识别反映自相似性尺度范围的无标度区。     

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.     

甘肃城镇体系地域空间结构研究

在分析甘肃城镇体系地域空间结构现状的基础上,运用分形理论和方法对甘肃城镇体系地域空间结构的聚集维数、网格维数和关联维数进行了测算和分析,表明甘肃城镇体系的空间分布是分形的,以14个主要城市为研究对象,甘肃省城市体系在空间分布上比较集中;以甘肃省内75个城镇为研究对象,城镇分布的总体均衡性适中;以中部城镇密集地区为研究对象,城镇体系在空间上分布比较均匀。并据此提出了甘肃城镇体系地域空间结构合理化的建议。     

Using Fractal Dimensions for Characterizing Intra‐urban Diversity: The Example of Brussels

The objective of this paper is to compare fractal‐based parameters calculated by different fractal methods for urban built‐up areas and to link the observed spatial variations to variables commonly used in urban geography, urban economics, or land‐use planning. Computations are performed on Brussels, Belgium. Two fractal methods (correlation and dilation) are systematically applied for evaluating the fractal dimension of built‐up surfaces; correlation is used to evaluate the fractal dimension of the borders (lines). Analyses show that while fractal dimension is ideal for distinguishing the morphology of Brussels, each estimation technique leads to slightly different results. Interesting associations are to be found between the fractal dimensions and rent, distance, income, and planning rules. Despite its limitations, fractal analysis seems to be a promising tool for describing the morphology of the city and for simulating its genesis and planning. The model is robust: it replicates the urban spatial regularities and patterns, and could hence fruitfully be integrated into intra‐urban simulation processes.     

快速城镇化背景下乡村聚落分形特征及影响因素研究——以广东省茂名市为例

本文基于分形理论,借助聚集维数、空间关联维数及形态维数,对茂名县域、市域及镇域乡村聚落分形特征进行研究,并从自然地理、人口、设施建设和经济发展方面构建指标体系,运用Pearson相关性分析法,探讨分形影响因素.研究表明:①乡村聚落呈多尺度、多分形特征.聚集性从市域到镇域呈从地理导向到行政导向的趋势,高城镇化水平地区聚集...     

江苏省粮食产量吸引子维数研究

以混沌理论为基础,对江苏省粮食单产时间序列用分形的方法进行了初步研究,从吸引子维数、Kolomogorov熵等方面分析了粮食单产变化的混沌性质。研究结果表明,江苏省1978-1997年粮食单产的时序分布具有分形特征,且单产的变化是一个确定性的低维混沌吸引子。要恰当地描述江苏省粮食单产发生系统,需要构造包含12个状态变量的动力学系统。     

吉林省城市体系等级规模结构研究

等级规模结构是城市体系的三大结构之一,其特征可以反映出城市在不同规模层次中的分布状况及城市人口集中或分散的程度,有助于认识城市体系发展所处的阶段。通过统计数据计算分析,运用分形理论,发现吉林省城市体系等级规模结构满足位序-规模分布规律,城市规模分布的均衡程度较高,中小城市比较发育,首位城市垄断作用不突出,缺乏大城市。在吉林省城市体系动态变化过程中,等级规模结构相对稳定且不断趋于集中。在此基础上提出重点培育通化、延吉等大城市;继续扩大长春规模,发挥整体效益;加强交通网络建设;加快矿业城市可持续发展等建议。     

基于分形理论的江苏省南通市城镇体系空间结构研究

基于非线性科学分形理论以及运用GIS相关软件,通过计算南通城镇体系的首位指数、中心城市吸引力以及城镇交通网络长度-半径维数、网络分枝维数,探讨了南通城镇体系等级规模结构分形、城镇体系空间关联性分形以及南通城镇交通网络分形特征,从描述城镇等级体系、城镇交通网络分布入手,通过对南通城镇具体区域指标的分析和处理,并以分形理论中的二城市指数、三城市指数、四城市指数和十一城市指数为定量依据,将分形理论引入城镇体系研究的实践中,结果表明:南通城镇体系空间结构呈现分形特征,从而有效验证了分形特征不仅存在于大城市空间结构,中等城市的城镇体系依然存在,进而为指导南通城镇体系空间上合理布局提供定量依据与决策参考,并据此提出了南通城镇体系空间结构合理化的建议。     

豫北地区城镇规模分布的分形研究

本文运用分形理论对豫北地区城镇体系要素规模分布的自相似性质和特征进行研究,指出了系统等级结构分形的半退化、要素规模分布的二元化、空间图式的差异性和时间演化的均衡趋向,分析了分维(帕累托指数)上升的利弊,给出了计算最佳哲夫指数(从而找出恰适分维)的数学方法,文章最后根据分形优化原理提出了豫北地区城镇规模的改善措施。     

东北地区城市体系分形结构的地理空间图式——对东北地区城市体系空间结构分形的再探讨

在前期工作的基础上,对东北地区城市体系空间结构的分形维数进行了分省、分区计算,然后借助各种不同的分维数值对东北三省城市体系的地理结构进行了区域差异分析,进而总结了几种对于城市体系具有普遍意义的分形空间图式,最后对东北地区城市体系空间结构的分形优化提出了若干建议。文章为城市体系空间结构的分形研究提供了一个完整的范例。     

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。     

Noninferior Bandwidth Line Simplification: Algorithm and Structural Analysis

Digital line simplification operators are an important preprocessing component of a spatial data handling system. Simplification operators are used to generalize digital line files because these files are encoded at one scale but the objects they represent can be displayed at many other scales. Most line simplification algorithms are heuristics that caricaturize lines by eliminating points representing redundant data or conversely retaining the characteristic points of a line that have a high informational content. This paper presents a noninferior simplification algorithm that produces an optimal caricature of an encoded line with respect to the bandwidth criterion that all deleted points must be within a prespecified distance of the simplified line. Results show that it is a practical alternative to existing bandwidth heuristics.     

陇东地区城镇等级规模结构的分形研究

城镇体系的分形研究是城市地理学研究的新方向。文章从分形理论在城镇体系研究中的应用入手,以豪斯道夫(Hausdorff)维数为依据,借助Zipf公式,对甘肃省陇东地区的城镇等级规模结构进行了分维测算,结果表明该区域城镇体系具有分形特征,说明分形理论适合陇东地区城镇等级规模结构的测算分析。在分形的基础上分析了本区城镇规模结构的分布特点及其存在的问题:①首位城市规模不突出,其经济带动和功能辐射力量薄弱;②中间位序的城镇分布过于集中,人口分布显得比较均衡;③陇东地区城镇体系建设缺乏区际空间规模结构的发展。最后基于分形理论的测算与分析结果,提出了陇东地区城镇体系结构和功能优化的建议。     

不同尺度乡村聚落景观的空间集聚性分形特征及影响因素分析——以江苏省镇江市为例

为分析乡村聚落景观空间结构的分形特征,以GIS为平台、土地调查数据为主要数据源,通过集聚维数,分别在县域、镇域和村域三个尺度上,分析了聚落体系空间集聚性的分形特征及其影响因素。结果表明:乡村聚落景观在空间结构上具有比较明显的分形特征;空间集聚性存在不同尺度分形特征的差异,同时丹阳市的镇和中心村的集聚性则明显小于句容市;不同尺度聚落集聚性出现明显的尺度特征,即中心村 > 镇 > 县城;地形是影响乡村聚落景观空间集聚性分形特征,表现为腹地内坡度越大,集聚性越强;交通网络的完善降低了乡村聚落对空间直线距离的依赖性。     

On the Fractal Measurement of Geographical Boundaries

This paper has two main objectives. First, we review and evaluate four different computational methods for measuring the “fractality” of cartographic lines: these are known as the structured walk, the equipaced polygon, the hybrid walk, and the cell count methods. Second, because previous research has restricted the focus of fractal measurement exercises to isolated physical entities, the subject of our empirical study concerns the urban area of Swindon, United Kingdom, that comprises a mosaic of contiguous land-use parcels. In technical terms, the results pinpoint some of the comparative strengths and weaknesses of the four methods, whilst our substantive conclusion is that fractal dimension appears to be a function of both scale and land-use type in our geographical study.     

京津冀交通路网结构特征及其演变的分形刻画

交通一体化是京津冀协同发展的基础和前提，合理的交通网络结构对提升城市群整体效能意义重大。本文基于1995-2030年多源交通路网数据，运用分形思想，研究京津冀以城市群为节点体系的交通路网空间结构特征及演化趋势。主要结论如下：①京津冀高等级路网仍有一定扩展潜力，交通网络整体等级结构尚不稳定，未达到一种优化的分形递阶状态。②各级路网空间分布具有自仿射特征，但各向异性扩展强度正在逐渐减弱，城镇化和交通一体化战略的实施正在促进各级路网逐渐向自相似的结构一体化方向演化。③交通路网空间结构演化与城镇用地结构不同步，可能与系统所处城镇化发展阶段有关。④高等级路网分维演化服从次数大于1的logistic模型，按照规划预期，各级路网空间发育将相继在2040年前后达到饱和；但按照规划设计高速公路建设将过度饱和，未来应及时调整规划。     

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.     

Regimes of ionospheric turbulence from fractal analysis of satellite radio signal scintillations

Samples of amplitude scintillations of the radio signal from a geostationary satellite obtained at a midlatitude station near Irkutsk were processed. For calculating the fractal dimensionalities the Grassberger and Procaccia [(1983) Physica D9, 189] algorithm was used. Results of the data processing tend to divide into two groups. One group includes those realizations for which it was possible to obtain reliable estimates of dimensionality. Three of the seven realizations considered were in this group, and the fractal dimensionalities were found to be low (3.12 4.5). The other data fall within the second group; a reliable estimate of dimensionality for them is unobtainable in terms of the method used. We suppose that this is attributable to the high dimensionality of the process. Power spectra of the signals of this group are close to those with an exponent of −2. The spectra of the signals of the first group are markedly steeper. On the basis of the data analyzed it is supposed that there exist two modes of ionospheric turbulence in midlatitudes, namely the mode with low dimensionality typical of localized turbulent processes, and the mode with high dimensionality typical of homogeneous turbulence that covers an extensive region of the ionosphere.     

华北平原农村居民点演变及社会经济影响因素分析

基于遥感图像分类解译数据,利用位序-规模模型、洛伦兹曲线、景观指数,定量识别了2000-2015年华北平原农村居民点空间分布、规模与形态演变特征,分析了社会经济因素的驱动机制。结果表明：华北平原农村居民点南-北方向呈显著的空间分异与集聚特征,密度分布呈现南密北疏的态势,与面积规模分布存在局域负相关;农村居民点景观指数显示出密度增大、形状更加规则、斑块面积差异增大、斑块间邻近距离不断缩短的变化特征;总人口数量和乡村户数等对农村居民点用地扩张具有促进作用,乡村常住人口、乡村从业人员数量等的作用为负。