## A FRACTAL VILLAGE

Enclosed, infinite, resilient architecture, inner courtyard, flood plain

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The project is inspired by the concept of enclosure, designed as a boundary between the interior and exterior, between inside and outside, between a chaotic city and an inner, sheltered courtyard. The system behind the layout of the village is inspired by a fractal formula, the Cantor function (Georg Cantor 1845-1918), which represents an example of a continuous function that grows to infinity. It is a system of expansion which, although unlimited, does not proceed in a linear fashion. On the contrary, it develops on the basis of centrality and takes the name of "Cantor dust"[1]. Applied to architecture, the mathematical principle highlights an unlimited expansion of the city, at the same time retaining the architectural element of the courtyard. The latter, which is a part of our tradition, in this case takes on extreme conditions to reach the size of a metropolis. Above all, however, the wall becomes an element that protects the living space from any flooding, which occurs increasingly in our country and is often the result of heavy rain or overflowing rivers. In fact, along the perimeter of the enclosure is a drainage system for waste and rain water, which passes through a purification plant into a large underground storage tank beneath the homes inside the actual enclosure. Once the water has been purified, it may be used by the village residents. Inside the enclosure, the space is protected and also contains a specific drainage system for both green and paved areas. Each basic enclosure contains four homes arranged in the four corners, 1.5 metres above ground level.

This expedient aims to protect the homes in the event of flooding, while allowing the courtyard to be admired as it transforms into a lake. The expansion of the enclosure will see an exponential increase in the size of the courtyard to 16 homes, and subsequently to 32, then 64 and so on. Each house measures 100 sqm and contains two bathrooms, three bedrooms, a dining-kitchen and a living room. The external wall enters the interior of each individual house and transforms into an element that divides the domestic spaces. The cold-pressed steel structure can be covered in various materials.

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[1] "Divide a given segment into three equal parts and remove the central part. Two segments remain: apply the same procedure to each one ad infinitum."The Cantor function is a continuous, increasing function (insofar as it is a uniform restriction of continuous functions), and is surjective from the interval [0, 1]. It is a restricted, but not absolutely continuous variation. It has a derivative of zero and is differentiable at every point other than on the Cantor set. It is, therefore, a constant function in every sub-interval of [0, 1,] which does not contain points of the Cantor set (the latter set measures zero], i.e. in the intervals of the (0.x1x2x3...xn022222..., 0.x1x2x3...xn200000...) type. Despite this, it is increasing (broadly speaking). The Cantor function, restricted to the Cantor set, is always continuous, growing and surjective on the interval [0, 1]: this implies that the Cantor set is uncountable. This function is useful to define a Peano curve, i.e. a curve that completely fills a square.

Architect:

Anna Rita Emili