Fractal Characteristics of the Distribution Pattern of Mangrove Bruguiera Gymnorrhiza Populations in Southern China

The distribution patterns of mangrove Bruguiera gymnorrhiza population s in southern China are analyzed using the box-counting method of fractal theory. The patterns of B. gymnorrhiza populations could be thought of as fractals as they exhibit self-similarity within the range of scale considered. Their fractal dimensions are not integer but fractional, ranging from 1.04 to 1.51. The unoccupied dimensions change from 0.49 to 0.96. The combined conditions of population density, pattern type and aggregation intensity together influence the values of fractal dimensions of patterns. The box counting is a useful and efficient method to investigate the complexity of patterns. Fractal dimension may be a most desirable and appropriate index for quantifying the horizontal spatial microstructure and fractal behaviors of patterns over a certain range of scales.

Rhythmic precipitate patterns and fractal structure

Liesegang patterns of parallel precipitate bands are obtained when solutions containing co-precipitate ions interdiffuse in a 1D gel matrix.The sparingly soluble salt formed,displays a beautiful stratification of discs of precipitate perpendicular to the 1D tube axis.The Liesegang structures are analyzed from the viewpoint of their fractal nature.Geometric Liesegang patterns are constructed in conformity with the well-known empirical laws such as the time,band spacing and band width laws.The dependence of the band spacing on the initial concentrations of diffusing（outer）and immobile（inner）electrolytes（A0 and B0,respectively）is taken to follow the Matalon-Packter law.Both mathematical fractal dimensions and box-count dimensions are calculated.The fractal dimension is found to increase with increasing A0 and decreasing B0.We also analyze mosaic patterns with random distribution of crystallites,grown under different conditions than the classical Liesegang gel method,and report on their fractal properties.Finally,complex Liesegang patterns wherein the bands are grouped in multiplets are studied,and it is shown that the fractal nature increases with the multiplicity.

Multifractal Simulation of GeochemicalMap Patterns

Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.

Introduction of Multiscaled Longitudinal Vortices by Fractal-Patterned Surface Roughness

To determine the type of surface roughness pattern that is suitable for adaptive suppression of the drag of an obstacle, we observed flow structures introduced by such obstacles. Several roughness patterns were tested: geometric patterns, fractal patterns, reptile-skin patterns, and patterns of circular cylinders arranged in a lattice and in a zigzag manner. A suitable pattern for adaptive control of flow is one that generates longitudinal vortices with nonconstant distances. The preferred instability mode of a laminar boundary layer is expected to be selected automatically from fluctuations involving many frequencies and caused by fractal patterns. Snake- and reptile-skin patterns may have a similar ability as fractal patterns because they consist of multiscale patterns. The longitudinal vortices generated from peculiar positions and concave corners in patterns were observed. The distance between these vortices is not constant because the onset of vortices is at concave corners in fractal patterns. These vortices have differing strengths and easily cause nonlinear interactions, so they can disturb a laminar boundary layer with several higher-harmonic frequencies. The velocity profiles of the laminar boundary-layer flow over the fractal patterns were measured by using hydrogen bubbles. The results show the down-wash flow between the longitudinal vortices, which means that the vortices may effectively suppress the boundary layer separation in an adverse pressure gradient.

Fractal features of soil profiles under different land use patterns on the Loess Plateau, China

Fractal theory is becoming an increasingly useful tool to describe soil structure dynamics for a better understanding of the performance of soil systems. Changes in land use patterns significantly affect soil physical, chemical and biological properties. However, limited information is available on the fractal characteristics of deep soil layers under different land use patterns. In this study, the fractal dimensions of particle size distribution（PSD） and micro-aggregates in the 0–500 cm soil profile and soil anti-erodibility in the 0–10 cm soil profile for 10 typical land use patterns were investigated in the Zhifanggou Watershed on the Loess Plateau, China. The 10 typical land use patterns were： slope cropland, two terraced croplands, check-dam cropland, woodland, two shrublands, orchard, artificial and natural grasslands. The results showed that the fractal dimensions of PSD and micro-aggregates were all significantly influenced by soil depths, land use patterns and their interaction. The plantations of shrubland, woodland and natural grassland increased the amount of larger micro-aggregates, and decreased the fractal dimensions of micro-aggregates in the 0–40 cm soil profile. And they also improved the aggregate state and aggregate degree and decreased dispersion rate in the 0–10 cm soil profile. The results indicated that fractal theory can be used to characterize soil structure under different land use patterns and fractal dimensions of micro-aggregates were more effective in this regard. The natural grassland may be the best choice for improving soil structure in the study area.

Using texture synthesis in fractal pattern design

Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)’s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood. Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern’s color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique.

基于分形图案的透孔织物的设计和开发

为了丰富花式透孔织物的花纹种类,利用平纹和透孔组织的特点,采用分形图案设计,将平纹和简单透孔组织结合,形成有规律的花式透孔组织图案,以谢尔宾斯基地毯图案作为花式透孔组织的分形图案纹样,进行花式透孔织物的组织设计、上机设计及工艺参数设计等,并进行试织。结果得出:采用谢尔宾斯基地毯图案作为分形图案进行纹样设计,使平纹和透孔组织形成的花式透孔组织图案更有规律性,同时纹样新颖,具有装饰性,分形图案的使用也为多组织组合形成多种类的透孔花纹图案提供了新思路。

基于参数化技术的图案设计综述

参数化、变量化技术是学术界、产业界的一个交叉学科研究热点。分析了包括形状语法、分形理论、数学模型等参数化图案设计的理论和方法,讨论与比较了建筑、产品以及图案设计3个领域的参数化设计语言。在此基础上,总结了在理论算法、设计流程以及参数化软件方面的共性,为图案设计的发展与多样性提供新的驱动力。针对服装图案特性,研究了参数化技术的应用现状与难题,提出了参数化技术在图案设计领域未来的发展方向。

基于Julia集的潮汕抽纱装饰纹样分形设计

分形普遍存在于自然环境的微观之中,在农业上常用于土壤特征与农作物结构等的分析。分形图案因其生于自然的特点,在解释自然结构的同时具有艺术性,与传统植物纹样搭配相适应。农作物作为潮汕抽纱纹样的主要题材,文章提出基于Julia集的潮汕抽纱植物装饰纹样分形设计模型,试图更好地实现潮汕抽纱数字化,提供符合当下审美的分形纹样设计,缓解自20世纪90年代工业化冲击后,抽纱从业人员凋零,缺乏从事其纹样设计人员的现状。通过对葡萄、麦穗、花卉等纹样进行归类与分形维度的计算,总结潮汕抽纱植物纹样的分形特征,应用分形艺术软件UF6完成分形纹样设计,与传统潮汕抽纱植物纹样遵循类别、形制进行组合。最后,针对青年群体进行模型输出结果的问卷调研,从民族性、创新性、艺术性、喜爱度验证分形引入潮汕抽纱的可行性,并邀请非遗工作者从生产角度做出评价。结果表明:潮汕抽纱可通过分形设计扩充新的纹样素材,青年群体希望潮汕抽纱能以局部装饰的形式融入日常应用的产品中。在生产上,根据应用于织品、印刷等不同需求,对分形纹样的复杂程度作出考量或简化,为刺绣织品图案的创新设计提供参考,展现分形通过农业所表现的艺术性。

分形理论在木材美学图案设计中的应用

木材花纹的自然属性决定了分形几何是用来描述木材花纹形态的最有力的武器之一,分形理论对于美学艺术研究具有深远意义。通过对分形几何的理论和特点进行研究,分析分形设计美学特征,导入红木木材宏观、微观构造图案进行设计,得到具有美学价值的纹理设计图案。以分形维数较高的檀香紫檀微观木材纹理构造图像为素材,应用Ultra Fractal 6分形软件对檀香紫檀构造图像进行分形设计,从而生成3种木材美学图案,再进行艺术设计得到具有规律与秩序感花纹图案,使之更具有装饰性,充分利用木材的非物质属性,丰富人们的精神文化生活,充分展现红木木材美学的应用价值。

分形艺术与传统中式纹样融合下的文创产品的商业应用

以分形艺术为出发点,结合中式传统纹样,将分形语言与中式传统纹样进行融合,得出理性和感性相结合的图案,同时将其运用于文创产品的实际应用中。

基于分形理论的青岛城市空间形态演化特征研究

随着滨海城市发展对集约化需求的增加,如何高效布局城市所处空间成为城市发展的关键。文章运用分形理论对青岛这一兼具“带形”与“环形”形态双重时空属性的滨海城市进行研究,并揭示其演变特征。结果显示:(1)青岛城市外部形态演变呈“轴带均衡集聚→环状多组团均衡分布”的演变趋势。(2)工业用地呈现均衡扩展趋势,商业与居住用地呈波动扩展的趋势。在此基础上提出相关建议,以期为青岛未来城市发展中明确空间发展方向与重点建设区域、提升用地资源的填充效率提供参考。

Experimental studies on the evolution process of microcrack patterns in concrete samples con-taining hard inclusions

Under biaxial pressure, the microcrack patterns of concrete samples with hard inclusion are as followings: Microcracks generate around the sample at the early pressured period, and gap is formed in the middle part with the increase of σ 1; microcrack gap is becoming smaller gradually with σ 1 increase again; microcracks become active within the original gap, but they in an original active area become small. Approaching the main fracture, microcracks form as a belt and jump back and forth in the belt. The spatial fractal D s of microcracks changes from small to big, but turns decrease when approaching the main fracture. All of the features were seldom mentioned in the past experiment, however, which have some similarities with the long seismicity patterns before strong earthquakes. In this paper, Lancang Gengma earthquake was taken as an example to analyse.〖KH*2D]

Visitor flow pattern of Expo 2010

Expo 2010 Shanghai China was a successful, splendid, and unforgettable event, leaving us with valuable experi- ences. The visitor flow pattern of the Expo is investigated in this paper. The Hurst exponent, the mean value, and the standard deviation of visitor volume indicate that the visitor flow is fractal with long-term stability and correlation as well as obvious fluctuation in a short period. Then the time series of visitor volume is converted into a complex network by using the visibility algorithm. It can be inferred from the topological properties of the visibility graph that the network is scale-free, small-world, and hierarchically constructed, confirming that the time series are fractal and a close relationship exists among the visitor volumes on different days. Furthermore, it is inevitable that will be some extreme visitor volumes in the original visitor flow, and these extreme points may appear in a group to a great extent. All these properties are closely related to the feature of the complex network. Finally, the revised linear regression is performed to forecast the next-day visitor volume based on the previous 10-day data.

Growth pattern of reed in Caogang Lake,Huanghuaihai Plain,China

The researches about reed growth were mainly concentrated on seasonal dynamics, investigation of reed resource, and comparison of different ecotypes of reed. By means of fractal geometric theory of non linear science, the fractal character of growth pattern of reed, for the purpose of quantitatively exploring the mechanism of reed growth was studied. The way to calculate fractal dimension of reed growth is box dimension (BD) and information dimension (ID). The results showed that the difference between two samplings in May and those among three samplings in June and later were not remarkable for both BD or ID. It was noted that the difference between samplings in and after May is significant. It was demonstrated that the fractal dimension of size distribution of reed ranged from 0 6235 to 0 8761 The distribution pattern could be statistically divided as two significant periods: the size of reed is quite well distributed at the beginning of reed growth (fractal dimension>0 8), but is irregular in the middle and later growth season (fractal dimension<0 7). These results are benefit to reach the goal of rational use of reed resources and to protect the biodiversity in wetland ecosystem.

Soil Aggregates and Fractal Features under Different Land Use Types in a Frequent Debris Flow Area

The stability of soil aggregates and the fractal characteristics of four typical land use types(farmland,grassland,woodland,and bare land) in the Jiangjiagou Ravine(Yunnan,China),a frequent debris flow occurring area,were studied according to the normal mean mass diameter and fractal theory.The present research showed that the stability of the soil aggregates was different for the different land use types.When the soil depth was 0-30 cm,farmland soil formed more aggregates with diameters greater than 0.25 mm,i.e.,the farmland soil was more stable than that of the other three land uses.When the soil depth was 30-45 cm,the order of stability of the soil aggregates was woodland > grassland > farmland > bare land.The fractal dimensions had a significant linear positive correlation with the amount of soil particles with diameters of <0.25 mm,and a significant negative linear correlation with the amount of soil particles with diameters of 0.25-0.5 mm,0.5-1 mm and 1-2 mm.Smaller fractal dimensions of the soil particles correlated with more stable soil aggregates.The fractal dimensions had a positive linear correlation with the soil bulk density and a negative correlation with the concentration of organic matter.These results showed that soil aggregates can be used as a parameter for characterizing the soil structures and properties.According to these results,the soil particle fractal dimensions could not only objectively characterize the stability of the soil structure but also could be used to indicate soil structure and properties.In addition,these results have great significance for the discussion of the comprehensive evaluation of soil.

Dense Fractal Networks, Trends, Noises and Switches in Homeostasis Regulation of Shannon Entropy for Chromosomes’ Activity in Living Cells for Medical Diagnostics

We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometry with nanometer spatial resolution. Experimental data present fluorescence of many ten thousands of cells, from different parts of body in each population, in various blood samples. Data is presented in histograms as frequency distributions of flashes in the dependence on their intensity. Normalized frequency distribution of information in these histograms is used as probabilistic measure for definition of Shannon entropy. Data analysis shows that for this measure of Shannon entropy common sum of entropy, i.e. total entropy E, for any histogram is invariant and has identical trends of changes all values of E (r) = lnr at reduction of rank r of histogram. This invariance reflects informational homeostasis of chromosomes activity inside cells in multi-scale networks of entropy, for varied ranks r. Shannon entropy in multi-scale DNA networks has much more dense packing of correlations than in “small world” networks. As the rule, networks of entropy differ by the mix of normal D 2 and abnormal D > 2 fractal dimensions for varied ranks r, the new types of fractal patterns and hinges for various topology (fractal dimension) at different states of health. We show that all distributions of information entropy are divided on three classes, which associated in diagnostics with a good health or dominants of autoimmune or inflammatory diseases. This classification based on switching of stability at transcritical bifurcation in homeostasis regulation. We defined many ways for homeostasis regulation, coincidences and switching patterns in branching sequences, the averages of H&ouml;lder for deviations of entropy from homeostasis at different states of health, with various saturation levels the noises of entropy at activity of all chromosomes in support regulation of homeostasis.

Fractal geometry and topology abstracted from hair fibers

Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the （3）-circle and the （9＋2）-circle fractal sets as subsets. As far as the （9＋2） topological patterns are concerned, the following propositions are proved： The （9＋2） topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent （or fundamental）. Besides, we demonstrate that the （3, 9＋2）-circle and （9＋2, 3）-circle fractal sets are golden ones with symmetry breaking.