The City in the City

A Fractal Pattern Language for Self-organizing Urbanism

Abstract

In 1975, the mathematician Benoît Mandelbrot coined the term fractal to refer to complex structures that contain self-similar elements repeating at different scales, which can be described with mathematical precision. He and other researchers found that many behavioral patterns in nature abide by this fractal structure—as do the physical surroundings of human environments. The purpose of this research paper is to use the pattern language of fractals—which exhibit characteristics of self-growth and self-adaptation—as a model for resisting urbanistic and capitalistic dogmas that govern contemporary city design. This paper draws lessons from a fractal reading of cities and communities that exhibit complex fractal logic and give credence to the notion that cities, by nature, are inherently complex and unpredictable.

As a theoretical underpinning for the research paper, the text bridges theories in fractal geometry from Mandelbrot, design theory from Christopher Alexander, and critical temporality from Denis Ferreira da Silva’s writings, in addition to other writings on fractal urbanism. Through these lessons, this paper concludes that the rituals, forms, and timelines in cities operate according to paradoxical but coherent logics—orthodox/fluid, predictive/generative, linear/recursive—and that fractal thinking can reconcile these paradoxes and guide more adaptive, autonomous urban futures. Ultimately, the text proposes a fractal city framework to imagine an ever-expanding series of rituals, forms, and timelines emerging autonomously from both within and without the metropolitan city of today—the City in the City.