Over the course of 6 months, students of the Computer Morphogenisis Lab at the Politecnico di Torino in Italy developed structures through the application of mathematics in architectural design. With the assistance of Karamba, they studied and analyzed fractal geometries which were then fabricated at 1:1 scale.

Text and Images from Iasef Md Rian:

*Students had selected and applied the concept of Fractal Geometry, a relatively new geometric system developed by Benoit Mandelbrot in the 1970s. Fractal geometry has unique characteristics of self-similar repetitions and the roughness or irregularity at multiple zooming scales. Mathematically, fractal shapes are the shapes that are not integer dimensional, but non-integer dimensional shapes. In this workshop, students developed a geometric model of a surface based on the fractal concept, which was neither a two-dimensional smooth surface nor a three-dimensional solid-like mesh. Their fractal surface was developed by following Takagi-Landsberg’s mathematical function of the fractal surface. This surface is transformed gradually from a smooth paraboloid surface to an unsmooth fractal surface. The shape transition was controlled by the parameter of Fractal Dimension (D _{H}). Students used Takagi-Landsberg’s fractal surface as a base for constructing a grid-shell structure which they named ‘FracShell’. *

Right: The roughness of the fractal surface can be controlled by a factor of relative size value, which is the factor of midpoint displacement value. This value is also related to the value of the fractal dimension. When the fractal dimension is 2.0, the surface becomes smooth and paraboloid, but when its fractal dimension value becomes more than 2.0, the surface turns into unsmooth, i.e., fractal.

*Before the construction, the team verified the structural capacity with Karamba. After passing the verification under self-weight, students started to construct the grid-shell completely manually without taking any help of robotic support or CNC. Fractal geometry has a unique quality of self-similarity, which means, each module is a scaled copy of its parent module, and that parent module is further scaled copy of its own parent module, and so on. Thus, this unique fractal scheme helped the students to develop a typical module first that was repeated, saving many hours of fabrication time.*

**Host University:** Politecnico di Torino

**Host Lab:** Computer Morphogenesis

**Tutors:** Iasef Md Rian, Mario Sassone, Shaghayegh Rajabzadeh

**Students: **Bruno Iorio, Leonardo Ramondetti, Elisa Pitassi, Samuele Marino, Leonardo Ramondetti, Gabriele Fusaro

**Funded by:** Politecnico di Torino’s Departmental Research Grant