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  • Thumbnail for The Fractal Structure of Cities: A Mathematical Approach to Urbanization
    The Fractal Structure of Cities: A Mathematical Approach to Urbanization by Verchota, Allie Milla

    The theory of fractal geometry is a relatively new concept in Mathematics. However, it is a concept humans are very familiar with. Most commonly we think about fractals as they relate to objects found in nature. For example fractal analysis can be used to define human structures like cities. We will focus on one way of defining and analyzing cities, by calculating their fractal dimension. This thesis will connect fractal dimension as it relates to city analysis via area and length. We will draw some conclusions regarding social implications of city life based on the theory of connectivity, fractal theory, and the parallel between connectedness and fractility. These types of questions will be open ended and allow for inquiries on further research into the science of cities.

  • Thumbnail for The Fractal Structure of Cities: A Mathematical Approach to Urbanization
    The Fractal Structure of Cities: A Mathematical Approach to Urbanization by Verchota, Allie Milla

    The theory of fractal geometry is a relatively new concept in Mathematics. However, it is a concept humans are very familiar with. Most commonly we think about fractals as they relate to objects found in nature. For example fractal analysis can be used to define human structures like cities. We will focus on one way of defining and analyzing cities, by calculating their fractal dimension. This thesis will connect fractal dimension as it relates to city analysis via area and length. We will draw some conclusions regarding social implications of city life based on the theory of connectivity, fractal theory, and the parallel between connectedness and fractility. These types of questions will be open ended and allow for inquiries on further research into the science of cities.