Abstract
Since Benoit Mandelbrot (1924–2010) coined the term “fractal” in 1975, mathematical theories of fractal geometry have deeply influenced the fields of landscape perception, architecture, and technology. Indeed, their ability to describe complex forms nested within each other, and repeated towards infinity, has allowed the modeling of chaotic phenomena such as weather patterns or plant growth. Some human-designed patterns such as the ones developed by Islamic cultures have been found to follow similar principles of hierarchy, symmetry, and repetition. However, the application of these principles in the design of gardens is an underexplored field. This paper presents a comparative exploration of the four-fold garden design model—the chahár-bágh—typical of Persian and Islamic garden design by analyzing two case studies: Taj Mahal and Isfahan’s city plan. This four-fold pattern is known to not only have a religious reading but to be also linked with ideals of fair distribution. Using an innovative compositional fractal analysis inspired by architecture, our results demonstrate that these gardens contain a high level of self-replication and scale invariance and that they exhibit a high fractal dimension. The novel application of this method of analysis to historical landscape plans allows us to assess to what extent fractal concepts were already in use before the European Renaissance and Mandelbrot’s explorations, and to speculate on their symbolism in the context of Islamic and Persian garden design. Specifically, we conclude that the fractal characteristics of these gardens might be intended as a representation of the infinite divine but also of principles of fairness and equality. Moving forward, this approach could be applied to design spaces, namely in the infrastructural design of the urban fabric, which are both meaningful and environmentally just.
Highlights
Fractal geometry is a theoretical framework formulated to unite forms and patterns previously considered too complex to be described (Mandelbrot, 1975)
Based on principles of selfsimilar symmetry and scale invariance, it is currently used in biological sciences such as medicine and ecology (Kenkel and Walker, 1996) as a way to understand complexity and structure chaos
The central square itself is magnified 24 times showing both self-similarity and scale invariance. Another approach to analysis would consider the square barred by a cross as a basic unit of the Taj Mahal gardens, just like the square with a missing center could be seen as the basic pattern behind the Sierpinski’s carpet, a famous fractal object described by Wacław Sierpiński in 1915 (Fig. 7)
Summary
Fractal geometry is a theoretical framework formulated to unite forms and patterns previously considered too complex to be described (Mandelbrot, 1975). The framework can be used to model natural forms such as coastlines and mountain ranges and blood vessels. It is sometimes considered a universal pattern language as the forms it describes can be found in every living thing (Di Leva, 2016). There is no doubt that much like the shapes it describes, “fractal geometry dates back to centuries before the emergence of the fractal theory by Mandelbrot” There is no doubt that much like the shapes it describes, “fractal geometry dates back to centuries before the emergence of the fractal theory by Mandelbrot” (Abdelsalam and Ibrahim, 2019, p. 27)
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