O objetivo do presente trabalho é a aplicação da teoria fractal na quantificação de perfis de rugosidade de juntas rochosas. Para esta quantificação digitalizaram-se perfis de rugosidade encontrados na literatura e posteriormente determinou-se a dimensão fractal de cada perfil utilizando três métodos. Dentre estes, estabeleceu-se que o método modificado do divisor é o mais adequado para determinar a dimensão fractal. Verificou-se também a importância do parâmetro de intersecção, que também pode quantificar o perfil de rugosidade. De uma análise comparativa se estabeleceu que o parâmetro de intersecção quantifica melhor o perfil que a dimensão fractal. Para uso prático, este parâmetro foi adimensionalizado e o novo parâmetro foi denominado como peso fractal. Este último junto com a dimensão fractal quantificam melhor o perfil de rugosidade. Avaliou-se também o comportamento da dimensão fractal, parâmetro de intersecção e peso fractal no efeito escala da rugosidade. Estes têm uma dependência do comprimento do perfil. / The purpose of the present work is the application of the fractal theory to the quantification of rock joint roughness. Rock joint roughness profiles available in the literature were digitized in order to allow quantitative analysis. The fractal dimension was determined for each profile using three different methods. Among those methods, it was found that the modified divider method is the most adequate. The importance of the intercept parameter was also found for the fractal dimension determination and roughness quantification. Based on a comparative analysis, the intercept parameter was found to be better for roughness quantification than the fractal dimension. For practical purposes, a dimensionless form of the intercept parameter was established. The new parameter was called the fractal weight. The joint use of both fractal dimension and fractal weight was found to be the most effective way to quantify rock joint roughness profiles. The influence of the three mentioned parameters on joint strength scale effect was also analyzed.

Many studies of natural landscape preference have demonstrated that qualities such as 'complexity' and 'naturalness' are associated with preference, but have struggled to define the key characteristics of these qualities. Recently, the development of software programs and digital techniques has offered researchers new ways of quantifying the landscape qualities associated with preference. Among them fractal geometry offers the most promising approach. Fractals have been defined as mathematical models of organic objects and patterns as opposed to the straight lines and perfect circles of Euclidean geometry found in man-made environments. Fractal patterns are mainly characterized by their dimension, which could be described as a statistical quantification of complexity. By applying this mathematical concept to digital images, several studies claim to have found a correlation between the fractal dimensions of a set of images and the images' preference ratings. Such studies have particularly focussed on demonstrating support for the hypothesis that patterns with a fractal dimension of around 1.3 induce better responses than others. However, much of this research so far has been carried out on abstract or computer-generated images. Furthermore, the most commonly used method of fractal analysis, the box-counting method, has many limitations in its application to digital images which are rarely addressed. The aim of this thesis is to explore empirically the suggestion that landscape preference could be influenced by the fractal characteristics of landscape photographs. The first part of this study was dedicated to establishing the robustness and validity of the box-counting method, and apply it to landscape images. One of the main limitations of the box-counting method is its need for image pre-processing as it can only be applied to binary (black and white) images. Therefore, to develop a more reliable method for fractal analysis of landscapes, it was necessary to compare different methods of image segmentation, i.e the reduction of greyscale photographs into binary images. Each method extracted a different structure from the original photograph: the silhouette outline, the extracted edges, and three different thresholds of greyscale. The results revealed that each structure characterized a different aspect of the landscape: the fractal dimension of the silhouette outline could quantify the height of the vegetation, while the fractal dimension of the extracted edges characterized complexity. The second part of the study focused on collecting preference ratings for the landscape images previously analysed, using an online survey disseminated in France and the UK. It was found that different groups of participants reacted differently to the fractal dimensions, and that some of those groups were significantly influenced by those characteristics while others were not. Unexpectedly, the variable most correlated with preference was the fractal dimension of the image's extracted edges, although this variable's predictive power was relatively low. The study concludes by summarising the issues involved in estimating the fractal dimensions of landscapes in relation to human response. The research offers a set of reliable and tested methods for extracting fractal dimensions for any given image. Using such methods, it produces results which challenge previous hypotheses and findings in relation to fractal dimensions that predict human preference, identifying gaps in understanding and promising future areas of research.

The Edwards aquifer lies in the structurally complex Balcones fault zone and supplies water to the growing city of San Antonio. To ensure that future demands for water are met, the hydrological and geophysical properties of the aquifer must be well-understood. Fractures often occur in a power-law distribution. Fracture distribution plays an important role in determining electrical and hydraulic current flowpaths. The thesis research presents an evaluation of the controlled-source electromagnetic (CSEM) response for layered models with a fractured layer at depth described by the roughness parameter, BV, such that 0</=BV, associated with the power-law length-scale dependence of electrical conductivity. A value of BV=0 represents homogeneous, continuous media, while a value of 0<BV shows that roughness exists. 1-D synthetic modeling shows that the existence of a fractured layer at depth is apparent in the CSEM time-domain response for models representing aquifers. The research also provides an analysis of the Seco Creek frequency-domain helicopter electromagnetic survey data set by introducing the similarly defined roughness parameter BH to detect lateral roughness along survey lines. Fourier transforming the apparent resistivity as a function of position along flight line into wavenumber domain using a 256-point sliding window gives the power spectral density (PSD) plot for each line. The value of ?H is the slope of the least squares regression for the PSD in each 256-point window. Changes in BH with distance along the flight line are plotted. Large values of BH are found near well-known large fractures and maps of BH produced by interpolating values of BH along survey lines suggest unmapped structure at depth.

The effects of environmental factors were investigated in fractal dimension (D) of Gracilaria tenuistpitata. G. tenuistipitata was cultured indoors under various factors for 30 days. Algal thalli were pressed on flat surface for photopraph with optical or digital camera to measure fractal dimension based on the relationship between levels and numbers of algal branch. Environment factors in this study were including illumination (L¡F 45~365£gmol¡Em-2¡Es-1), water flow (F¡F 80~900L¡Eh-1), temperature (T¡F 10~35¢J) and salinity (S¡F 10~50 ppt). The results of ANOVA and General linear models showed that illumination, temperature and salinity but water flow significantly affected thallus fractal dimension with the maximum at 255£gmol¡Em-2¡Es-1, 19¢J and 24 ppt respectively, The cross reactions between environment factors did not significantly affect the fractal dimension, reflecting that environment factors affect the appearance of G. tenuistpitata independently. The effect of environment factors on biomass of G. tenuistpitata was studied in each experiment and the results showed that all environment factors tested in this study significantly affected the biomass of G. tenuistpitata.

In this thesis, the relation between the fractal structure and the performance of the antennna is discussed. From the simulation and theoretical analysis , we can conclude that the 10dB impedance bandwidth of the monopole decreases when the iteration level of the fractal structure increases . Then we use the fractal structure to design the LTCC antenna. We design and manufacture an LTCC antenna for WLAN IEEE 802.11a. The simulation and measured results are analyzed and discussed. Finally, we provide a new method which can reduce the cross polariztion level. And this method is used to reduce the cross polarization of the monopole using the second iteration level of the Minkowski curve. It is shown that the method does work from the measurement. This method can reduce the cross polarization of the fractal antenna and hence find more application in communication systems.

Snapping shrimp is the well-known source of biological sound in subtidal zone. Sounds were created by imploding a cavitation bubble which is generated under the tensile forces of the claw after a high-velocity water jet has been formed. The sounds of snapping shrimp is not only for attacking and defending, but also for communicating with each others. These sounds thus become the material of studying complex behavior arisen from interaction between individuals. This paper studies the change of fractal dimension of snapping shrimp¡¦s noises in different condition of environment. Sounds of snapping shrimp in Chigu lagoon and Tanshui estuary were recorded respectively. With the help of computer software to edit and calculate, the fractal dimension was taken as indicator for the complexity of communication. The behavior was assumed to be affected by many factors at the same time. Analysis of multiple regression with fractal dimension as dependent variables show that the fractal dimensions increased with night time, water temperature, and the ebb tide, but decrease with light intensity. Diurnal hour is the most significant factor in Chigu area. Analysis of Tanshui¡¦s data showed fractal dimension decrease with water depth.

With the advent of multimedia computer, the voice and images could be stored in database. How to retrieve the information user want is a heard question. To query the large numbers of digital images which human desired is not a simple task. The studies of traditional image database retrieval use color, shape, and content to analyze a digital image, and create the index file. But they cannot promise that use the similar index files will find the similar images, and the similar images can get the similar index files. In this thesis, we propose a new method to analyze a digital image by fractal code. Fractal coding is an effective method to compress digital image. In fractal code, the image is partitioned into a set of non-overlapping range blocks, and a set of overlapping domain blocks is chosen from the same image. For all range blocks, we need to find one domain block and one iteration function such that the mapping from the domain block is similar to the range block. Two similar images have similar iterated functions, and two similar iterated functions have similar attractors. In these two reasons, we use the iteration function to create index file. We have proved fractal code can be a good index file in chapter 3. In chapter 4, we implement the fractal-based image database. In this system, we used fractal code to create index file, and used Fisher discriminate function, color, complexity, and illumination to decide the output order.

With the advent of multimedia computer, the voice and images could be stored in database. How to retrieve the information user want is a heard question. To query the large numbers of digital images which human desired is not a simple task. The studies of traditional image database retrieval use color, shape, and content to analyze a digital image, and create the index file. But they cannot promise that use the similar index files will find the similar images, and the similar images can get the similar index files. In this thesis, we propose a new method to analyze a digital image by fractal code. Fractal coding is an effective method to compress digital image. In fractal code, the image is partitioned into a set of non-overlapping range blocks, and a set of overlapping domain blocks is chosen from the same image. For all range blocks, we need to find one domain block and one iteration function such that the mapping from the domain block is similar to the range block. Two similar images have similar iterated functions, and two similar iterated functions have similar attractors. In these two reasons, we use the iteration function to create index file. We have proved fractal code can be a good index file in chapter 2. In chapter 3, we implement the fractal-based image database. In this system, we used fractal code to create index file, and used Fisher discriminate function, color, complexity, and illumination to decide the output order.

Recent theoretical and empirical advances, in particular the fractal branching model of West, Brown and Enquist (WBE model), have highlighted the importance of exchange surfaces in understanding the integration of whole plant form, and functional traits. Key insights have arisen from an increased understanding of how the properties of distributive vessel networks influence whole plant metabolic and physiological traits. Here I show that an extension of WBE model, one in which network geometry is continuously variable, provides a robust foundation to understand the diversity of scaling relationships in plants and the organs of which they are composed. Central to the original WBE model has been the assumption of energy minimization as a selective force shaping the evolution of internal and external plant surface areas and morphology. Here I demonstrate how additional selection on traits not detailed in the original WBE formulation can lead to departures from strict energy minimization, and can thus explain much of the variation and covariation in observed scaling central tendencies in plant gross morphology observed within, and across natural plant communities. I test the predictions from this model extension with data from both regional and global datasets, from the leaf to whole plant level, across herbaceous, succulent, woody, annual and perennial taxa. These data demonstrate that the model extension is quite robust and should serve as a foundation upon which more detailed future models can be constructed.

Stokes’ law that is traditionally used for modeling the sedimentation of flocs, incorrectly assumes that the floc is solid and spherical. Consequently the settling rates of flocs cannot be estimated using the Stokes law. The application of fractal dimensions to study the internal structure and settling of flocs formed in lime softening process was investigated. An optical microscope with motorized stage was used to measure the fractal dimensions of lime softening flocs directly on their images in 2 and 3D space. The fractal dimensions of the lime softening flocs were 1.15-1.27 for floc boundary, 1.49-1.90 for cross-sectional area and 2.55-2.99 for floc volume. Free settling tests were used for indirect determination of 3D fractal dimension. The measured settling velocity of flocs ranged from 0.1 to 7.1 mm/s (average: 2.37 mm/s) for the flocs with equivalent diameters from 10µm to 260µm (average: 124 µm). Floc settling model incorporating variable floc fractal dimensions as well as variable primary particle size was found to describe the settling velocity of large (>60 µm) lime softening flocs better than Stokes’ law. Settling velocities of smaller flocs (<60 µm) could still be quite well predicted by the Stokes’ law. The variation of fractal dimensions with lime floc size in this study indicated that two mechanisms are involved in the formation of these flocs: cluster-cluster aggregation for small flocs (>60 µm) and diffusion-limited aggregation for large flocs (<60 µm). Therefore, the relationship between the floc fractal dimension and floc size appears to be determined by floc aggregation mechanisms. The settling velocity of lime softening flocs was also modeled by a general model that assumes multiple normally distributed fractal dimensions for each floc size. The settling velocities were in the range of 0-10mm/s and in good agreement with measured settling velocities (0.1-7.1mm/s). The Stokes’ law overestimates the settling velocity of lime flocs. It seems that the settling velocity of flocs is mainly controlled by aggregation mechanisms and forming large floc does not guarantee improved sedimentation. The multifractal analysis of lime softening flocs showed that these aggregates are multifractal and a spectrum of fractal dimensions is required to describe the structure of an individual floc.