Abstract
In early phases of design, during the process of form-exploration, architects -- knowingly or unknowingly -- have used mathematics as their guiding tool to evolve a formal methodology of design. Fundamental compositional principles such as symmetry, rhythm and proportion are based on specific mathematical underpinnings. However, very often the designer comes across a situation where these underlying mathematical principles need to be overlapped or interfaced. Applying fractal concepts to the order can accommodate this complex diversity. Fractals allow us to provide a combination of order and surprise in a rhythmic composition using a specific mathematical geometry. Fractals are typically unit-based and, can thus allow exploration in architectural designs which have a ‘unit’ as a fundamental issue or necessity. The design of housing layout stands out prominently among such architectural problems and, can thus be one such instance in which fractals may be used as a design tool. Commonly seen organisational patterns in housing layout designs create rigidity and monotony, while others like clustered groups are too inconsistent and can create disorder. The research tries applying fractal ordering principles to strike a balance between these extremes by creating an orderly arrangement of houses with an underlying variation in the pattern. The traditional processes of creating housing layouts is quite cumbersome. With the mathematical power of computers, fractal ordering principles are used as Iterative functions to generate multiple design options. The research investigates the potential of the emergent patterns of fractals as an organisational principle in designing housing layouts, while limiting it based on site constraints, size and the transforming rules. In doing so, the objective is to explore the computational and mathematical basis of repetitive patterns in architectural order and compositions. The study also aims at developing a computer application, based on algorithms using fractals, which offers capabilities as a conceptual and organisational tool for a housing layout. The application is implemented, tested and its results are demonstrated using a live terrain data.
Highlights
In housing layout design, typically, dwelling units are created by the same sequence of rules, based on the form of a generic house
The research starts with a premise that when this theory is applied to housing layout patterns, the resulting variation could capture the recursive and the complex rhythms of fractals
These ideas are focused to the use of the Sierpinski Triangle to create a set of organisational principles that will be applied to the generative system to create the growth patterns in a housing layout design
Summary
In housing layout design dwelling units are created by the same sequence of rules, based on the form of a generic house. Repetitions of identical or similar forms create a predictable pattern [21] This configuration is comparable to that of a typical self-similar fractal. Mitchell (1989), in his work, compares the theory of fractal geometry to a system of rules that can manipulate patterns of recursive elements to create architecture [14]. Creating housing layouts using principles of a Sierpinski Gasket can make the design more coherent by relating the scale of the overall layout to that of the smaller housing units. The occurrence of the house on the site in the fractal pattern would depend on the organising principles of the Sierpinski Gasket and the local conditions of the site
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