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A map combines scientific facts with aesthetic perceptions. This study argues that scaling is universal in mapping reality and evoking a sense of beauty. Scaling laws are used to reveal the underlying structures and dynamics of spatial features. Complex systems, such as living cities involve various interacting entities at all scales. Each individual coherently interacts and overlaps with others to create an unbreakable entity. Scaling structures are also known as fractals. Fractal geometry is used to depict a complex system. Natural objects, such as trees, contain a similar geometry (branches) at all scales. This study attempts to effectively visualize the scaling pattern of geographic space. In this regard, the head/tail breaks classification is applied to visualize the scaling pattern of spatial features. A scaling pattern underlies a geographic space. Visualizing the scaling structure using the head/tail breaks classification can further evoke a sense of beauty. This kind of beauty is on the structural level and was identified by Christopher Alexander, who asserted that beauty is not a personal experience but objectively exists in any space. Alexander developed the theory of centers to broaden the concepts of life and beauty.  A structure with a scaling property (with recursive centers) has high quality of life, and a scaling pattern has positive effects on individual’s psychological and physical well-being. To verify the concept of objective beauty, human beings are used as measuring instruments to examine the assumptions. This study adopts the mirror-of-the-self test to examine human reactions to 23 pairs of images, including photographs of buildings and two types of map. The idea is that participants sense the quality of life by comparing a pair of objects and selecting the object that presents a better picture of themselves. Once individuals feel the self in a picture, they are able to detect real beauty. In this manner, individuals can detect real beauty and life that deeply connect to their inner hearts. The tests were conducted through personal interviews and Internet surveys with the public and with professionals, and 392 samples were collected. The study results show that more than 60% of the individuals selected images with a scaling pattern. These results are in accordance with Alexander’s assumption. In particular, more than 65% individuals selected maps that depict scaling forms. Moreover, this study conducted a training test with a particular group of individuals, after which more than 70% of individuals selected scaling maps. The results reveal that scaling laws are applicable for creating maps and evoking a sense of beauty.

The design implications of chaos theory are explored. What does this theory mean, if anything, to landscape architecture or architecture? In order to investigate these questions, the research was divided into four components relevant to design. First, philosophical- chaos offers a nonlinear understanding about place and nature. Second, aesthetical-fractals describe a deep beauty and order in nature. Thirdly, modeling-it is a qualitative method of modeling natural processes. Lastly, managing- concepts of chaos theory can be exploited to mimic processes found in nature. These components draw from applications and selected literature of chaos theory. From these research components, design implications were organized and concluded. Philosophical implications, offer a different, nonlinear realization about nature for designers. Aesthetic conclusions, argue that fractal geometry can articulate an innate beauty (a scaling phenomenon) in nature. Modeling, discusses ways of using chaos theory to visualize the design process, a process which may be most resilient when it is nonlinear. The last research chapter, managing, applications of chaos theory are used to illustrate how complex form, like that in nature, can be created by designers. / Master of Landscape Architecture

The U.S. Coast Guard maintains a network structure to connect its nation-wide assets. This paper analyzes and models four highly aggregate traces of the traffic to/from the Coast Guard Data Network ship-shore nodes, so that the models may be used to predict future system demand. These internet traces (polled at 5â 40â intervals) are shown to adhere to a Gaussian distribution upon detrending, which imposes limits to the exponential distribution of higher time-resolution traces. Wavelet estimation of the Hurst-parameter is shown to outperform estimation by another common method (Sample-Variances). The First Differences method of detrending proved problematic to this analysis and is shown to decorrelate AR(1) processes where 0.65< phi1 <1.35 and correlate AR(1) processes with phi1 <-0.25. The Hannan-Rissanen method for estimating (phi,theta) is employed to analyze this series and a one-step ahead forecast is generated. / Master of Science

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El paisaje, concebido como una unidad espacial y temporalmente pluriescalar caracterizada por unos patrones de distribución - una estructura-, unas funciones y una red de flujos de materia, energía e información (Forman y Godron, 1986), constituye un modelo apropiado para estudiar el territorio (Marull, 2002). En la presente investigación se hace un análisis de los cambios ocurridos en la estructura del mosaico paisajístico de la comarca de l´Alt Empordà entre 1957 y 2001, para ellos se divide la comarca en unidades paisajísticas basadas en criterios fisiográficos determinados a escala 1:25000. El análisis de la estructura paisajística de las diferentes unidades paisajísticas se ha realizado a través de indicadores de composición y de estructura según clases paisajísticas (cubiertas o usos del suelo), mediante el cálculo y análisis de indicadores de estructura desarrollados por la ecología del paisaje, los cuales, han permitido caracterizar y analizar las transformaciones en el tamaño, la forma y el arreglo espacial de los parches tipo que configuran el mosaico paisajístico. Para el proceso de cálculo y análisis espacial se han empleado los sistemas de información geográfica (SIGs), el programa Patch Analyst 1.2. La información cartográfica se elaboró a partir de ortofotomapas digitales y fotos aéreas generados por el ICC, así como de fuentes secundarias.Además, el trabajo incluye una aplicación teórico-metodológica a la identificación de redes ecológicas a través del uso de indicadores, así como el uso de inventarios fitosociológicos en la evaluación de hábitats borde. / Landscape is conceptualized as a pluriscalar spatial and temporal unit, characterized by distribution patterns -structure- function and a net of flows of matter, energy and information giving territorial dynamics (Forman y Godron 1986), which permits us study territories from a ecosystem approach (Marull, 2002).This research is concern with the changes in the landscape structure of the comarca Alt Empordà between 1957 and 2001. In order to conduct the analysis, the territory was divided into landscape units based on physiographic criteria using a map scale of 1: 25 000. The structure of each landscape unit was then calculated and analysed based on cover and landuse classes (patches) using fractal indicators such as type of patch, size, form and spatial distribution. The analysis was conducted by using aereal photographs developped by the Instituto Cartográfico de Cataluña, geographic information systems and the sofware Patch Analysist 2.1.In addition, this reaserch includes a landscape ecologypcal approach identifying econets throw the use of different structure indicators. Forthemore, it incorporates an analysis of edge habitats based on phytosociologic information.

CAPES / Este trabalho traz uma breve apresentação histórica do surgimento dos Fractais, bem como do criador do termo Fractal, Benoit Mandelbrot. Aqui são apresentados alguns Fractais clássicos e destacam-se suas principais propriedades Matemáticas. Sugere-se um software livre, e de acesso online, para a criação dessas figuras. Posteriormente, aplica-se uma proposta didática baseada em um material paradidático que propõe a investigação de Fractais nos anos finais do ensino fundamental ou no ensino médio, relatando-se os resultados dessa aplicação. / This dissertation presents a brief historical overview of the origins of Fractals, as well as of the creator of the Fractal term, Benoit Mandelbrot. Some classical Fractals are presented and its main mathematical properties are highlighted. It suggests a free software, with on-line access, to the creation of these figures. Later, the didactic proposal is applied based on a paradidactic material, which proposes investigation of Fractals in the last years of primary school or in the secondary school and the results of this application are reported.