a pictorial of Kunstformen der Natur by Ernst Haeckel, mentioned in previous posts, have been a great inspiration to stereometric a study on models and their deformations. The research developed within the firm Zaha Hadid Architects during the design of the museum of the Mediterranean of Reggio Calabria, was the opportunity to experiment with compositional techniques inspired by evolutionary biology and is fully described by Filippo Innocenti in growth, form and fit "(1).
The analysis was conducted in a scientific manner by applying simple transformations to forms of organic inspiration generated by precise rules of Euclidean geometry. The morphogenesis of the form starts from the basic polygon in the first case an equilateral triangle. On each side of the triangle were made of squares, in turn divided into two equal parts by the axis of symmetry, and the medians of the triangle, until a sort of cross with three branches. On top of this geometric shape evenly distributed control points of the curves of the third degree that will be generating three-dimensional shapes represented in these pictures.
The possible configurations are endless, and each can be an unlimited number of transformations. You can choose square, pentagon polygon ol'esagono as the basis of the process instead of the triangle, you can use curves instead of third and second grade can have their control points in a different way on the vertices of the polygon base. In the same way that "every natural phenomenon is the summation of a infinite number of shares subject "(2), the transactions that take place during the whole deformation process are many and the result can never be considered the final stage but a precise snapshot of a complex system in constant transformation.
The extraordinary properties of these systems is to maintain their morphological characteristics unchanged even after substantial changes in geometry. As in the Cartesian grid of D'Arcy W. Thompson each of these forms can be obtained through a deformation of another form that has the same geometric structure, and by convention is taken as a reference model. For example, starting from the basic shape of five-lobed configurations can be obtained by applying simple transformations of translation or rotation of some control points of the curves. In some of the above cases the changes were made according to principles of axial symmetry or center, others in a free manner, but all are easy to observe well attributed to the element pentalobato start and keep unchanged the major morphological features.
(1) eda Examples of Architecture - Architecture Info. The performative Architecture of the Information Age.
(2) D'Arcy W. Thompson - On Growth and Form, the geometry of nature
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