Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potentia...Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potential of fractals in traditional textile design,a fractal-based generative framework was proposed for efficiently creating drawnwork patterns suitable for practical handicraft production.The research was initiated with an analysis of the structural composition of center,skeleton,and filler motifs extracted from a pattern sample library.Based on this hierarchical classification,the box-counting method was employed to calculate their respective fractal dimensions.Building on fractal art theory,generative algorithms,and studies on the application of Ultra Fractal,a Chaoshan drawnwork fractal design model was established.Using this model,51 drawnwork fractal patterns and 153 handkerchief patterns were generated.These patterns were subsequently applied in real-world production to validate the feasibility and value of fractal techniques in textile design.展开更多
The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley...The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong ＂roll-off＂ effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size （metal tonnage） is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.展开更多
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 disc...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.展开更多
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 va...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.展开更多
Our serial studies from {dy1970}s on chemical composition, structure determination and formation mechanism of gallstones were reviewed. The chemical component investigation of brown-pigment gallstone demonstrated that...Our serial studies from {dy1970}s on chemical composition, structure determination and formation mechanism of gallstones were reviewed. The chemical component investigation of brown-pigment gallstone demonstrated that it consists of macromolecules such as proteins, glycoproteins, polysaccharides, bilirubin polymers and pigment polymers, and biomolecules such as cholesterol, bile salts, calcium salts of carbonate, phosphate, fatty acids and bilirubinate as well as various metal ions. The binding of metal ions with bile salts and bilirubin plays important roles in gallstone formation, i.e., calcium bilirubinate complex is the major constitute of brown-pigment gallstones, and copper bilirubinate complex is critical in the black color appearance of black-pigment gallstone. The cross section of many gallstones exhibits a concentric ring structure composed of various small particles with a fractal character. This is nonlinear phenomenon in gallstone formation. Atypical model system of metal ions-deoxycholate (or cholate)-gel was chosen to mimic an in vitro pattern formation system. The experimental results suggested that a nonlinear scientific concept should be considered in understanding gallstone formation. Minor changes in the chemical composition and/or the microenvironment may lead to very different precipitate patterns with a variety of shapes, colors, appearances, and structures. A new model was suggested that periodical templets of periodical and fractal patterns were formed in the initial stage, then the spatio-temporal patterns grew gradually on it. Furthermore, the interaction between divalent metal ions and bile saltsin vitro was investigated, and the results indicated that non-stoichiometric M(DC)2-NaDC mixed complexes with mixed micelles structure can be formed in physiological condition.展开更多
文摘Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potential of fractals in traditional textile design,a fractal-based generative framework was proposed for efficiently creating drawnwork patterns suitable for practical handicraft production.The research was initiated with an analysis of the structural composition of center,skeleton,and filler motifs extracted from a pattern sample library.Based on this hierarchical classification,the box-counting method was employed to calculate their respective fractal dimensions.Building on fractal art theory,generative algorithms,and studies on the application of Ultra Fractal,a Chaoshan drawnwork fractal design model was established.Using this model,51 drawnwork fractal patterns and 153 handkerchief patterns were generated.These patterns were subsequently applied in real-world production to validate the feasibility and value of fractal techniques in textile design.
基金supported by Geological Survey of Canada and China University of Geosciences (Wuhan)
文摘The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong ＂roll-off＂ effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size （metal tonnage） is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70871082)the Shanghai Leading Academic Discipline Project, China (Grant No. S30504)the Science and Technology Innovation Foundation of Shanxi Agricultural University, China (Grant No. 201208)
文摘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.
基金the National Natural Science Foundation of China (Grant Nos. 29671002, 39730160 and 20023005) and the State Key Project for Fundamental Research of MOST (Grant No. G1998061370).
文摘Our serial studies from {dy1970}s on chemical composition, structure determination and formation mechanism of gallstones were reviewed. The chemical component investigation of brown-pigment gallstone demonstrated that it consists of macromolecules such as proteins, glycoproteins, polysaccharides, bilirubin polymers and pigment polymers, and biomolecules such as cholesterol, bile salts, calcium salts of carbonate, phosphate, fatty acids and bilirubinate as well as various metal ions. The binding of metal ions with bile salts and bilirubin plays important roles in gallstone formation, i.e., calcium bilirubinate complex is the major constitute of brown-pigment gallstones, and copper bilirubinate complex is critical in the black color appearance of black-pigment gallstone. The cross section of many gallstones exhibits a concentric ring structure composed of various small particles with a fractal character. This is nonlinear phenomenon in gallstone formation. Atypical model system of metal ions-deoxycholate (or cholate)-gel was chosen to mimic an in vitro pattern formation system. The experimental results suggested that a nonlinear scientific concept should be considered in understanding gallstone formation. Minor changes in the chemical composition and/or the microenvironment may lead to very different precipitate patterns with a variety of shapes, colors, appearances, and structures. A new model was suggested that periodical templets of periodical and fractal patterns were formed in the initial stage, then the spatio-temporal patterns grew gradually on it. Furthermore, the interaction between divalent metal ions and bile saltsin vitro was investigated, and the results indicated that non-stoichiometric M(DC)2-NaDC mixed complexes with mixed micelles structure can be formed in physiological condition.
