Fractal analysis of the Orce skull sutures

Methods of fractal geometry (Mandelbrot, 1983) are used here to analyse the relative complexity of the sagittal and lambdoid sutures visible in the skull fragment formed by parts of an occipital squame and parietals found in a sealed deposit at the early Lower Pleistocene site of Venta Micena (Orce, Granada, Spain), generally regarded as human bone but occasionally suggested as belonging to an equid. For comparison with the fossil, corresponding sutures of various primates (hominids, pongids and cercopithecids) and two other groups of mammals (equids and ruminants) were analysed using the computer program FRACTAL-D (Slice, 1989) in order to determine their fractal dimensions as a measure of differential sutural design complexity. The results show that the fractal dimension of the Venta Micena skull sutures lies within the range of variation for infant specimens of both modern and Plio-Pleistocene hominids. Sutural complexity in young pongids and cercopithecids overlaps the range of fractal dimensions found in hominids, whereas values obtained from equids and ruminants are significantly greater than those for all the primates analysed here. Therefore, in terms of fractal dimension measures of relative complexity, the sutures preserved in the Venta Micena fossil could not have belonged to an equid (pace Agusti & Moyà-Sola, 1987); rather, its fractal dimension is consistent with the attribution of the fossil to an infant of Homo sp.     

退化沙质草地开垦和围封过程中的土壤颗粒分形特征

研究了科尔沁退化沙质草地开垦和围封过程中土壤颗粒分形维数的变化特征,以及分形维数与土壤性状的关系.结果表明,不同开垦和围封年限的土壤颗粒分形维数(0～30cm)介于2.387～2.588之间.随着开垦年限的增加,0～15 cm层土壤颗粒分形维数从2.441降至2.387;围封11年后,0～15 cm层土壤颗粒分形维数增加到2.588.15～30 cm层土壤颗粒分形维数无明显变化.土壤颗粒分形维数是反映土壤质地的一个较好指标,重点反映粘粒含量,其次是粉粒含量.分形维数的变化能够很好地表征退化沙质草地土壤的化学、物理和生物学性状的变化趋势,可以作为评价退化沙质草地土壤性状的一个综合指标.     

Nonlinear fractal dynamics of human colonic pressure activity based upon the box-counting method

The computational fractal dimension of human colonic pressure activity acquired by a telemetric capsule robot under normal physiological conditions was studied using the box-counting method. The fractal dimension is a numeric value that quantifies to measure how rough the signal is from nonlinear dynamics, rather than its amplitude or other linear statistical features. The colonic pressure activities from the healthy subject during three typical periods were analysed. The results showed that the activity might be fractal with a non-integer fractal dimension after it being integrated over time using the cumsum method, which was never revealed before. Moreover, the activity (after it being integrated) acquired soon after wakening up was the roughest (also the most complex one) with the largest fractal dimension, closely followed by that acquired during sleep with that acquired long time after awakening up (in the daytime) ranking third with the smallest fractal dimension. Fractal estimation might provide a new method to learn the nonlinear dynamics of human gastrointestinal pressure recordings.     

The Quasi-Fractal Structure of Fish Brain Neurons

The box-counting method for calculating the fractal dimension (D) with the ImageJ 1.20s software is used as a tool for quantitative analysis of the neuronal morphology in the fish brain. The fractal dimension was determined for several types of neurons in the brain of two teleost species, Pholidapus dybowskii and Oncorhynchus keta. These results were compared with those obtained for some neurons of the human brain. The fractal (fractional) dimension (D), as a quantitative index of filling of two-dimensional space by the black and white image of a cell, is shown to vary from 1.22 to 1.72 depending on the type of neuron. The fractal dimension reaches its maximum in less specialized neurons that carry out a number of different functions. On the other hand, highly specialized neurons display a relatively low fractal dimension. Thus, the fractal dimension serves as a numerical measure of the spatial complexity of the neuron and correlates with the morphofunctional organization of the cell.     

红树植物木榄种群高度结构的分形特征

 采用计测等值线分形维数的方法,探讨山口国家级红树林自然保护区内的木榄(Bruguiera gymnorrhiza)种群高度结构的特征。结果表明,木榄种群的高度结构具有分形的特征,其计盒维数介于1.61～1.90之间,信息维数介于1.63～1.84之间,分形维数的高低主要与幼树个体的数量、个体的集聚程度和高度层次结构的复杂程度等密切相关。计盒维数定量描述种群占据垂直空间的能力和程度,而信息维数揭示种群高度层次细节的尺度变化强度和个体高度分布的非均匀性程度。分析表明,等值线法能够有效地表征木榄种群高度结构的分     

科尔沁沙地农田沙漠化演变中土壤颗粒分形特征

研究了科尔沁沙地农田沙漠化过程中土壤的粗粒化和养分的贫瘠化特征 ,土壤颗粒分形维数的变化特征 ,以及分形维数与土壤性状的关系。结果表明 :土壤沙粒含量越高 ,土壤分形维数越低 ,表征农田沙漠化程度越高 ;土壤颗粒分形维数与土壤有机 C、全 N、粘粉粒含量之间存在显著的线性关系。说明分形维数能很好地表征农田沙漠化演变中土壤结构和养分状况以及沙漠化的程度 ,可作为评价土壤沙漠化演变的一项综合性定量指标。     

Fractal dimensions of cranial sutures and waveforms.

Two quite different shapes of cranial sutures ostensibly yield fractal dimensions. The rare, intricate sutures yield the more valid fractal dimensions because self-similar scaling provides a double-log plot of negative slope. These sutures are fractals over a range of several r values. Some of the highly folded, wavy sutures in humans also fill space except at very tiny values of r, but are nonfractal. A great deal depends on whether the dimension D is > 1 and by how much, whether the curve yields a false fractal dimension, whether the curve scales and shows self-similarity, and whether the scaling occurs regularly in the same pattern. We suggest careful attention to the inverse power law equations, which when misused can yield false fractal values. Cranial sutures vary from the simple wavy sutures to the complex folded ones, and, in rare instances, evolve and develop to the self-similar, scaling, elaborate ones called intricate sutures. The main thing is to express the biology precisely, whether waveform regularity or irregularity or scaling elaboration conserving space and the original shape. D values may not in themselves reliably allow such a distinction, by whatever method used.     

基于盒维数的心音信号分形特征研究

在传统盒维数的基础上,从尺度变化的角度,提出一种计算心音信号时域波形分形维数的新的二进盒维数算法,并给出了算法思想和估算方法;然后用该方法对正常心音和几种典型的病态心音的分形维数进行计算,并对其分形特征进行了研究．研究结果表明：心音信号具有明显的分形特征,分形维数能够反映心音信号的复杂程度,并且能够明显地区分正常心音和病态心音．     

褐飞虱(Nilaparvata lugens)发生的分形性质研究

运用分形理论以安徽省庐江县植保站和江苏省吴县值保站1979～1990年及太湖地区农科所1986～1998年间褐飞虱发生的田间系统调查资料为例,对褐飞虱发生的性质进行了探讨。结果表明：(1)庐江站、吴县站和太湖地区农科所褐飞虱发生在一定标度域内具有分形性质。其分维值分别为0．7158、0．52l2和0．2816;(2)褐飞虱发生的分维值是表征一定标度区间的发生程度差异的一个新的参数,分维值大,则发生程度轻,反之则重(3)分维数D值与褐飞虱发生的聚集程度是密切相关的,D值小聚集程度大,反之聚集程度小,D值可以作为褐E虱聚集分布程度的一个指标;(4)褐飞虱发生具有多重分形结构,其广义维数谱Dq曲线可以用于褐飞虱发生的预测预报。     

Modelling applicability of fractal analysis to efficiency of soil exploration by roots

BACKGROUND AND AIMS: Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis of roots. In this study, fractal analysis was applied to the study of root architecture and acquisition of diffusion-limited nutrients. The hypothesis that soil depletion and root competition are more closely correlated with a combination of fractal parameters than by any one alone was tested. MODEL: The geometric simulation model SimRoot was used to dynamically model roots of various architectures growing for up to 16 d in three soil types with contrasting nutrient mobility. Fractal parameters were calculated for whole roots, projections of roots and vertical slices of roots taken at 0, 2.5 and 5 cm from the root origin. Nutrient depletion volumes, competition volumes, and relative competition were regressed against fractal parameters and root length. KEY RESULTS: Root length was correlated with depletion volume, competition volume and relative competition at all times. In analysis of three-dimensional, projected roots and 0 cm slices, log(fractal abundance) was highly correlated with log(depletion volume) when times were pooled. Other than this, multiple regression yielded better correlations than regression with single fractal parameters. Correlations decreased with age of roots and distance of vertical slices from the root origin. Field data were also examined to see if fractal dimension, fractal abundance and lacunarity can be used to distinguish common bean genotypes in field situations. There were significant differences in fractal dimension and fractal abundance, but not in lacunarity. CONCLUSIONS: These results suggest that applying fractal analysis to research of soil exploration by root systems should include fractal abundance, and possibly lacunarity, along with fractal dimension.     

云贵鹅耳枥种群分布格局的分形特征

应用分形理论中的计盒维数和信息维数探讨了贵阳喀斯特山地贵鹅耳枥种群分布格局的分形特征。结果表明,贵鹅耳枥种群的分布格局具有分形特征,其计盒维数为1．1853－1．7419,信息维数为1．1961－1．7051。集群型的贵鹅耳枥种群的计盒维数和信息维数均比随机型的高。计盒维数定量地反映了贵鹅耳枥种群占据生态空间的能力,信息维数则揭示了该种群格局强度的尺度变化程度和表征了种群个体分布的非均匀性。这两种维数方法都适用于贵鹅耳枥种群分布格局分形特征的定量描述。     

黑土表层土壤颗粒的分形特征

基于第二次全国土壤普查结果,应用土壤颗粒的质量分布计算了36个典型剖面表层土壤颗粒的分形维数值.结果表明:土壤颗粒分形维数值D在2.5831～2.8230,其变异性极弱,且分形维数值随质地变细而增大;土壤机械组成中,砂粒(2～0.02mm)含量、粉粒(0.02～0.002mm)含量与分形维数值均呈显著负相关(P<0.05);粘粒(<0.002mm)含量与土壤分形维数值呈极显著正相关(P<0.01);分形维数值D与土壤中的有机质、全N、全P、全K含量及pH值相关性均不显著.土壤分布的分形维数可以作为反映黑土退化程度的一个综合性定量指标.     

天然黄山松种群格局的分形特征——计盒维数与信息维数

采用计盒维数和信息维数对屏南和寿宁不同群落的天然黄山松(Pinus taiwanensis)种群格局的分形特征进行比较分析.结果表明,天然黄山松种群格局具有分形特征,其计盒维数值在1.299 8～1.862 6之间,不同群落的大小次序为Q3>Q1>Q2>Q4>Q7>Q8>Q5>Q6;信息维数值在1.205 7～1.863 7之间,大小次序是Q3>Q1>Q2>Q4>Q8>Q7>Q5>Q6,屏南天然黄山松近纯林黄山松种群的计盒维数和信息维数均高于寿宁混交林,计盒维数定量描述种群占据水平空间的能力和程度,信息维数揭示种群格局强度的尺度变化及个体分布的非均匀程度,分形维数值的高低与群落环境、种群密度、种群在群落中的优势地位、个体的聚集程度及幼树个体数量等相关.黄山松种群格局分形维数随海拔呈现上下波动变化,1 250～1 270 m是更适生的海拔范围.此外,黄山松种群格局的分形特征存在一定的尺度范围,其拐点尺度是分形范围的下限尺度.     

山东泰山地区景观结构变化及其分形分析

将泰山风景区划分为 8个区域 11个基本景观类型 ,包括松林、栎林、刺槐林、侧柏林、针阔叶混交林、经济林、灌丛、裸岩、荒地、水体、建筑。在此基础上 ,利用 3S技术和分形理论对各个景观要素进行了分析 ,并讨论了景观特性及其变化的分形性质。结果表明 :(1)分维值的大小反映了景观斑块面积、斑块数量和平均斑块面积等因素的相互作用 ,在一定尺度下分维的大小反映了区域内景观斑块的不规则程度和复杂程度 ,斑块越不规则、越复杂 ,其分维越大 ,反之亦然。在泰山地区 ,自 1986年至 2 0 0 1年 ,刺槐林一直保持着较高的分维值 ,其它景观类型的分维值则差别不大 ,而针阔叶混交林的分维值变化较大 ;(2 )森林景观受多种因子的影响 ,在高海拔区域主要受垂直地带性规律影响为主 ,在旅游区主要受人类活动的影响为主 ,15 a来各个区域分形维数的总体变化趋势相似 ;(3)大部分区域在 2 0 0 1年的景观多样性、破碎度高于 1986年的 ,而景观优势度则略为下降     

桂花叶片的分形特征

提供了一种叶片分形维数的测定方法,并用其测定了桂花(Osmanthus fragrans Lour)的叶片分形维数。通过分析发现：(1)桂花叶片具有典型的分形特征并且这种分形特征可以用分形理论的一般方法加以研究;(2)同一株桂花树的成熟叶片在统计意义上具有相同的分形维数;(3)对于桂花这个物种的成熟叶片在统计意义上具有相同的分形维数。由此推测同一种植物的成熟叶片(或者其他构件)具有相同分形维数。最后提出创建植物分形分类学的设想。     

Radiographical study of skull fragment of Venta Micena (VM-0) (Orce, Granada Spain)

Since 1983, the Orce skull has been a polemic piece. The last article which refuses the human affinity of VM-0 is based on the presence of a supposed coronalis suture in VM-0 situated at 40mm of lambda point (Moyà-Solà &; Khöler 1997). This would imply that VM-0 belonged to a very small skull not possible in human genus. The present detailed x-ray study which includes: “classic x-ray”, digital x-ray, macro x-ray and computerized tomography, proves definitively the not presence of coronalis suture in VM-0 and demonstrate that all interpretations based on the presence of coronalis suture are a great mistake. Also this study shows different characters which prove the human affinity of VM-0: presence of a wide sulcus sagittalis (9mm), the print of the superior sinus sagittalis where drained venous blood of a big brain is not possible in a colt whose brain size is similar to that of sheep. We consider that the visual inspection is not enough in human Palaeontology and it is incorrect to not apply the different tests which permit proving or refusing the different subjective impressions.     

青藏高原不同草地利用方式对土壤粒径分形特征的影响

研究青藏高原草地土壤粒径结构分形特征,为该地区土壤质量评价和生态恢复提供科学依据。以青藏高原4种高寒草地(放牧、围栏禁牧、围栏禁牧+补植、未干扰)为对象,采用分形理论,研究不同利用方式对高寒草地土壤颗粒组成及分形特征的影响,明确土壤粒径分形特征的影响因素。结果表明：与放牧和围栏禁牧+补植相比,围栏禁牧草地中黏粒和粉粒体积分数分别增加了60%—91.1%、43.5%—80.1%,禁牧能够促进土壤砂粒向黏粒和粉粒转变。不同草地利用方式对分形维数有显著影响,单重分形维数D值依次为放牧草地<围栏禁牧+补植草地<未干扰草地=围栏禁牧草地,多重分形维数,包括信息维数D₁、信息维数/容量维数比值D₁/D₀和关联维数D₂依次为放牧草地<围栏禁牧+补植草地<围栏禁牧草地<未干扰草地。单重分形维数D与土壤黏粒、粉粒呈极显著正相关(P<0.01);砂粒、黏粒、粉粒、有机碳和全氮是多重分形维数的限制因素。信息维数D₁、信息维数/容量维数比值D₁...     

桂花叶片的分形特征

提供了一种叶片分形维数的测定方法,并用其测定了桂花(Osmanthus fragrans Lour)的叶片分形维数。通过分析发现:(1)桂花叶片具有典型的分形特征并且这种分形特征可以用分形理论的一般方法加以研究;(2)同一株桂花树的成熟叶片在统计意义上具有相同的分形维数;(3)对于桂花这个物种的成熟叶片在统计意义上具有相同的分形维数。由此推测同一种植物的成熟叶片(或者其他构件)具有相同分形维数。最后提出创建植物分形分类学的设想。     

高寒草地甘肃臭草根系分形结构的坡向差异性

根系分形结构是植物根系构型应对环境异质性的表型可塑性结果, 可反映植物对生长环境的适应策略。利用ArcGIS建立研究区域的数字高程模型, 并提取坡向数据, 采用全根挖掘和Win-RHIZO根系分析仪相结合的方法, 研究了祁连山北坡高寒退化草地不同坡向甘肃臭草(Melica przewalskyi)的根系分形结构。结果表明: 随着坡向由北坡向东坡、西坡、南坡转变, 草地群落的密度、高度和土壤含水量逐渐减小, 甘肃臭草种群的密度、高度以及根系分形丰度呈逐渐增大的趋势、分形维数逐渐减小; 不同坡向甘肃臭草根系分形维数和分形丰度间的相关性存在差异(p < 0.05), 南坡和北坡甘肃臭草根系分形维数分形丰度之间存在极显著负相关关系(p < 0.01), 东坡和西坡之间存在显著负相关关系(p < 0.05), 甘肃臭草根系分形维数和分形丰度存在着“此消彼长”的权衡关系; 随着坡向由北坡向东坡、西坡、南坡转变, 甘肃臭草根系分形维数和分形丰度回归方程的标准化主轴(SMA)斜率逐渐增大(p < 0.05), 说明在干旱的南坡, 根系所开发利用的相同体积的土壤内, 根系分支更少、更稀疏。不同坡向甘肃臭草合理权衡根系分形维数和分形丰度的资源配置模式, 体现了植物根系构型构建的资源投资权衡机制。