Fractal Analysis and Its Applications in Urban Environment

Fractal sets have been known for more than a century. However, only in 1975, Mandelbrot gave them the name “fractal” and mathematically defined them as sets whose Hausdorff dimension exceeds the topological dimension. While initially fractals were a pure mathematical phenomenon, afterwards fractal-like properties have been discovered in many natural and artificial objects and processes. The recently developed fractal analysis and theory of fractals have been applied in many different areas, including biology, health care, urban planning, environmental studies, geology, geography, chemistry, ecology, astronomy, computer science, social science, music, literature, art to name a few. This chapter gives a literature survey of the fractal theory and analysis applications to solve different problems in various areas. We describe main concepts and frequently used methods to compute a fractal dimension. Finally, we apply the fractal analysis to study the geography and infrastructure of Kyiv and facilitate decision making in urban planning.