Fractal cities: Looking closer at chaotic design
By Lauren MacDonald, Environmental Science and Chemistry, 2022
Navigating an older city can be confusing and harrowing, with winding alleyways and impossible shortcuts. But despite their chaotic reputation, cities like London, Paris, and Berlin are actually extremely well-organized when viewed through the lens of fractals.
Fractals are defined as recursive geometric figures that can be modeled mathematically, where each iteration of the fractal is mathematically similar to itself. That is, if you were to zoom in an infinite amount, the fractal would still appear identical. Fractals are present in nature (in snowflakes and conch shells), can be used to predict biological growth, and are frequently used in art by painters such as Jackson Pollock. They are also used in computer modeling systems to create complex computer-generated image (CGI) backgrounds that look realistic, as well as other computational uses.
In order to create a fractal, a model would start with an initiator shape (Image 0). The initiator would then be replaced with an altered version, called a generator shape (Image 1). After the alteration, any part of the image that is mathematically similar to the initiator shape will be replaced by the generator. Repeating this process infinitely will generate a fractal. (The fractal in Image 4 is the well-known Sierpinski’s Gasket.)
Fractals are present in nature (in snowflakes and conch shells), can be used to predict biological growth, and are frequently used in art by painters such as Jackson Pollock.
From a macro perspective, fractals can often seem just as chaotic and confusing as older cities. But when you zoom in, you find that there is actually a high degree of order present in the self-similarity. The world’s oldest cities — ones that were built without modern urban planning — fit this definition. When cities were first built in medieval times, they were designed with the intention that everyone could easily walk to everything they needed. Housing, shops, bathrooms, recreational facilities, and all other necessities were organized around central hubs. As the city grew, more space was needed. These small modules of all the necessities grew outwards, forming a maze-like city full of tiny alleys interconnected by larger central pathways.
In this way, older cities simulate fractal growth. Stereotypically “structured” cities like New York fail to have the same detailed organization as fractal cities. Today, we are used to navigating and understanding block cities because they make sense on a macro scale, but ancient cities were built on the micro scale when the only mode of transportation was walking. So, counterintuitively in the present day, these chaotic cities can be just as organized and easily understood as New York.
