摘要：fractal theory and regression analysis were employed for the first time to investigate the effect of pore size and pore distribution on high-temperature mechanical properties of porous alumina ceramics （PAC）. In the present work, PAC with the comparable porosity, different pore sizes and pore distributions were prepared using carbon black as the pore-forming agent. Particular emphasis in this study was placed on the establishment of correlation between the thermal shock resistance and pore properties. The relationship between fractal dimension （Df） and thermal shock resistance parameter （l？st） in specimens presented the negative power function, indicating that low Df could benefit the improvement of thermal shock resistance in specimens. The results showed that the increase of pore size and pore sphericity leads to a reduced Df, the enhanced hot modulus of rupture （HMOR） and Rst. The decrease of proportion of micro-pores below 2 μm, the increase of mean pore size and pore sphericity could result in the decrease of Dr, and then improve Rst and HMOR of specimens. Based on the correlation between Rst and pore characteristics, PAC with improved thermal shock resistance could be achieved when their pore structure meets the above features.

摘要：In the research of fractal cities, the fractal dimension is very important. It is used to describe the fractal character of the city. The authors have designed two approaches to calculate the fractal dimension by the box-counting method through an example of Beijing, which are called the vector method and the grid method, respectively. The former calculates the fractal dimension through an intersecting analysis in ArcView; and the latter is carried out by programming in Matlab. They are compared from three aspects： the calculating process, the limits in use, and the results. As a result, the conclusion is made that there are merits and faults on both methods, and they should be chosen to use properly in practical situation.

摘要：This article presents a novel image interpolation based on rational fractal fimction. The rational function has a simple and explicit expression. At the same time, the fi＇actal interpolation surface can be defined by proper parameters. In this paper, we used the method of ＇covering blanket＇ combined with multi-scale analysis; the threshold is selected based on the multi-scale analysis. Selecting different parameters in the rational function model, the texture regions and smooth regions are interpolated by rational fractal interpolation and rational interpolation respectively. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance compared with the state-of-the-art interpolation algorithms, especially in image details and texture features.

摘要：Non-destructive testing （NDT） has been widely used in many fields, we can easily see it is being used in shipbuilding, aerospace, weapons manufacturing and so on. ICT is one of the best non destructive testing methods currently, but it has not been used widely, because it requires much compute and costs much time. Defect location is one of the most important processing steps in the digital image analysis. Defect location would correspondingly reduce the time spent in the testing. We may only require locating the defects in some case. So, we divide the CT images into several little blocks which the square is equal, and then calculate the fractal on each block. By determining the value and connected region number of the fractal dimension, we can locate defects of the image. The results show that the block ffactal dimension is a useful and time-saving defect location method.

摘要：We present a method for computed tomography(CT)image processing and modeling for tibia microstructure,achieved by using computer graphics and fractal *** the large-scale image data of tibia species with DICOM standard for clinical applications,we take advantage of algorithms such as image binarization,hot pixel removing and close operation to obtain visually clear image for tibia *** of these images are based on 20 CT scanning images with 30μm slice thickness and 30μm interval and continuous changes in *** each pore,we determine its profile by using an improved algorithm for edge ***,to calculate its three-dimensional fractal dimension,we measure the circumference perimeter and area of the pores of bone microstructure using a line fitting method based on the least ***,we put forward an algorithm for the pore profiles through ellipse *** results show that the pores have significant fractal characteristics because of the good linear correlation between the perimeter and the area parameters in log–log scale coordinates system,and the ratio of the elliptical short axis to the long axis through ellipse fitting tends to *** on support vector machine and structural risk minimization principle,we put forward a mapping database theory of structure parameters among the pores of CT images and fractal dimension,Poisson’s ratios,porosity and equivalent *** this basis,we put forward a new concept for 3D modeling called precision-measuring digital expressing to reconstruct tibia microstructure for human hard tissue.

摘要：Chinese ice-ray lattices are perhaps one of the earliest and controlled designs of asymmetric and complex patterns applied as a traditional motif in *** intricate and complex designs developed centuries back have created an evident curiosity to explore its underlying geometric *** scholars used the Shape Grammar as a tool to explain and recreate similar *** previous studies conceive the ice-ray lattice design as the iterative subdivisions of a ***,they missed explaining this geometric quality through the discussion of fractal geometry,which can explain the shapes consuming selfsimilar or self-affine repetitions of itself at different *** a novel approach,this paper analytically focuses on the fractal characters of ice-ray lattice designs and uses fractal geometry as a unique tool for generating different types of ice-ray *** significance of this study is the demonstration of the efficacy of fractal geometry and the simple geometric rule of IFS for analyzing and algorithmically modeling complex lattices and cracked-like patterns.

摘要：The relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus of field unsaturated expansive soil in Nanning, Guangxi Province, China, was obtained by a direct or indirect method. Digital images of expansive soil of the surface fissure with different moisture contents were analyzed with the binarization statistic method. In addition, the fissure fractal dimension was computed with a self-compiled program. Combined with in situ seepage and loading plate tests, the relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus was initially established. The surface fissure ratio and moisture content show a linear relation, ＂y=-0.019 1x＋1.028 5＂ for rufous expansive soil and ＂y=-0.07 1x＋2.610 5＂ for grey expansive soil. Soil initial seepage coefficient and surface fissure ratio show a power function relation, ＂y=1× 10^-9exp（15.472x）＂ for rufous expansive soil and ＂y=5× 10^-7exp（4.209 6x）＂ for grey expansive soil. Grey expansive soil deformation modulus and surface fissure ratio show a power fimction relation of ＂y=3.935 7exp（0.993 6x）＂. Based on the binarization and fractal dimension methods, the results show that the surface fissure statistics can depict the fissure distribution in the view of two dimensions. And the evolvement behaviors of permeability and the deformation modulus can indirectly describe the developing state of the fissure. The analysis reflects that the engineering behaviors of unsaturated expansive soil are objectively influenced by fissure.

摘要：In Comparison with the traditional point-by-point line generation method,the method we present is based on segment code in Pan-Euclidean geometric space and is quite different in re- spect of running speed and theoretical *** paper presents an approach of using segment code to draw straight lines and shows the characteristics of a digital *** is a newly proposed al- gorithm applicable in CAD.