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Fractal Geometry is a branch of mathematics dealing with patterns that repeat themselves at different scales, leading to intricate and complex shapes. It lies at the intersection of several mathematical fields, including topology, measure theory, and functional analysis. In Functional Analysis, fractals can be studied using various techniques such as spectral theory or harmonic analysis. For instance, one might investigate how the properties of a fractal affect its associated operator or function space. Fractals have also found applications in science beyond mathematics, particularly in modeling natural phenomena like turbulence, coastlines, and biological systems. Thus, studying Fractal Geometry can shed light on both abstract mathematical structures and real-world complexities.