FRACTALITY
Exploring Fractals and chaos theory through its physical manifestations.
Personal interest project.
What is a fractal?
A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Fractal geometry is what cosmic systems like the structure of galaxies are based on.
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The Fractals of the Gangetic Plain. Smaller streams merge into tributaries, which merge into the river, which finally merges into the ocean. An example of self similarity across scales.
Fractals and Biology
Platonic geometry is what human made forms are based on, such as cuboids and pyramids. Biological life, however structures itself based on fractal geometry. The way trees take form, starting from the trunk, to the branches, to the twigs, to the leaves, they are all self similar structures, all based on the simple act of repeating the basic form of a line across scales, to give us the beautiful and infinitely various forms of trees. All life on this planet is based on this structural system and basic code. Using a simple form and repeating it across scales, this is what gives us the complex and 'rough' world we live in.
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Ferns are one of the earliest types of plants to evolve. The simplicity of the fractals in the form of this plant is easy to see.
The nautilus shell is also based on fractal geometry. The basic system is of a curve that has been repeated, but a little bigger each time. This coincides with the growth of the cephalopod itself. The golden ratio also organically occurs from this fractal.
The geometry of humans too, are fractal. The way our limbs grow in the embryo, the veins in our body, the bronchi in our lungs,and the structure of our neurons, are all fractal.
Fractals vs Platonic forms
Humans have always found beauty in platonic forms such as cuboids, pyramids and spheres. The evolution of mathematics and geometry is heavily influenced by the study of these forms, especially in the west. The discovery and articulation of fractals in mathematical terms is a relatively new occurrence. The term 'fractal' was first used by mathematician Benoit Mandelbrot in 1975. Thereafter, slew of explorations of the fractal forms and its applications took place.
A Mengers Sponge, seen on the left, and a section cut through it diagonally. Counter intuitively, the spaces in between are star shaped, not square.
A wonderful example of fractaliized platonic forms is a Mengers Sponge. Dividing each face of a square into 9 equal squares, and removing the centre one, makes the shape. Doing this with each remaining square, on all faces of the cube, makes the Mengers Sponge. This process can be repeated infinitely.
The area of a Mengers Sponge tends to infinity, and its volume tends to zero. Hence it does not exist in 3 dimensions, but in 2.3 dimensions.
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What if a housing complex were designed with this form? The continuous access to open space from the central void to the corners would allow for high densities without compromising on adequate light and ventilation. The form would also allow for services to run in a highly efficient manner.
Fractals in Architecture
While the western school of thought based its understanding of the universe on reducing its complexity to platonic philosophy and form, Asian and African cultures embraced the complexity of the fractal. Evidence of the articulation of fractals are seen in both Asian and African philosophies. This of course, manifests in their art and architecture as well. Right from the form of the buddhist rock cut Chaitya Halls, the shikara in temples, the tiling patterns in mosques, to the village layout and art of Zambian culture. The influence of fractal thought is abundant.
Fast forwarding to modern day, the state of architecture is at a crossroads. No longer is age old dialectic of form vs function relevant anymore. The relevance of the stoic architect that is removed from their context and only deals with pure form or pure function is also slowly dying out. There is the need for a new understanding of how we build and inhabit space, and fractals point to the answer.
The way nature manifests is through the fractal. It is in nature that we see the perfect meld of form and function, so well that there is no difference.
For example,The way the tree is shaped allows for maximum efficiency in transport of resources, both from root to leaf and leaf to root. The form also allows incredible structural integrity. With the load of all the leaves and branches being supported and transferred to the trunk and roots.
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How can we start thinking of a form of living and building space in fractal method? How can we think of human systems that function like natural systems, closed loop and maximizing efficiency through form and structure?
These are some of the questions I ponder in my free time.
Fractals in the decorative muqarnas vaulting in the iwan entrance to the Shah Mosque in Isfahan, Iran.
Fractal pattern in layout of the Ba-Ila Village settlement in southern Zambia.
The shikara of a temple is formed by the self similar scaled repetition of the elongated dome.
Microhousing Competition
Competition organized by Volume Zero. The brief was to design a housing complex for 100 people, with each house being maximum 400 sqft. This was an opportunity to exercise some of the concepts mentioned above.
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Co participants: Sayalee Golatkar and Kahin Vasi
Generative Microhousing
Often associated with complex mathematics, fractals are nature’s original form-building mechanism - creating some of the most diverse organisms with a very simple set of commands: scale up/down, rotate, repeat. To use fractals in design, we must understand human life, social interaction, production and economy - as fractals. We must understand how smaller units of society form larger clusters, and space, therefore, is adapted from the smallest individual function to the largest community programs.
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Designing for migrant workers at Mumbai’s docks, different types of worker families have been taken into account, as well as the building technology they’re familiar with and the spaces necessary for multiple families to gather and create an internal community and self-sufficient closed-loop economy.
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Where the pedagogy of housing philosophy revolves around floor-space-indexes and bare standards of living, we want to create a new, generative design methodology that can use the fractal commands to generate form, and also generate spaces that foster a communal lifestyle. Using fractal commands, we’re able to create units, clusters, super-clusters and mega-clusters - with scales increasing at every level. Within this framework, we create spaces that encourage sustainable living, are almost entirely self-sufficient, and allow rural migrants to reconnect with their community.
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