![]() ![]() ![]() These include, for example, self-similar, self-affine and random structures, dimension theory as well as projection and slice theorems. The program covers a variety of currently active research objectives and techniques to study open significant problems in fractal geometry - most of them closely related to dynamics. The field of modern dynamics emerged in the mid 1960's, and since then, dynamical methods have proved to be extremely efficient in many fields of modern analysis. In recent years there has been a remarkable interaction between fractal geometry and dynamics. Examples of the mutual enrichment include dynamics, mathematical physics, probability theory, calculus of variations, Fourier analysis, partialÄifferential equations, complex analysis, number theory, and potential theory. If youre interested in a broader mathematical perspective, I suggest beginning with Falconers Fractal Geometry: Mathematical Foundations and Applications followed by Falconers Techniques in Fractal Geometry (more applied oriented) or Edgars Integral, Probability, and Fractal Measures (more pure oriented). The ever-widening interest in fractals has greatly invigorated other fields of mathematics, and on the other hand, other areas of mathematics have contributed to the enrichment of fractal geometry. Examples of such objects include various types of generalised surfaces, ranging from rectifiable sets to currents and varifolds, and fractal type sets and measures, for example, attractors of dynamical systems and related invariant measures. Classification of Intrusion Detection Using Data Mining Techniques. The fundamental research theme is to study and apply general geometric objects which are often so irregular that the methods of classical analysis are unsuitable or inefficient. Effect of noise determination on estimation of fractal dimension of digital images. But if one considers the structures that are present in nature, that which are beyond the realm of smooth human construction, many of these rules disappear. Fractal geometry is a part of modern mathematical analysis. This classical, or Euclidean, geometry is perfectly suited for the world that humans have created. For modern computer graphics, the access to these techniques, combined with ray tracing allow to create incredible landscapes and effects. ![]() The mathematics of fractals has been enjoying an explosion of interest recently. ![]()
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