Symmetry by simplexity is a project of IaaC, Institute for Advanced Architecture of Catalonia developed at Master in Advanced Computation for Architecture & Design in (2020/2021) by: Students: Krishnanunni Vijayakumar, Keshava Narayan Faculties: Arthur Mamou-Mani


The project began with explorations for inspirations from natural and mathematical systems as a base for design. For this exercise the chosen inspirations were of the symmetrical repetitions of a kaleidoscope and ruled surfaces.
Kaleidoscope generates complex symmetric geometrical designs from small objects of simple geometry and colour.Symmetry and repetition offers the possibility of solving one module in terms of constructability, and repeating/ reflecting this units / modules to create livable spaces. Repetition can also lead to sustainability as the formwork used to build one module can be repeated to build the other modules hence saving money, material as well as time. Kalideoscope offers may folds of symmetry and repetition and though the images are adial when clipped in different forms gets rid of the strong centrality that the form proposes and hence can be a possible inspiration for producing complex forms. The reason for choosing a kaleidoscope is because it is less complex than that of crystallography but however can be used to produce interesting forms The next step was to identify a unit to be repeated/reflected. A unit based on mathematical ruled surface was derived as this base unit. A ruled surface can be described as the set of points swept by a moving straight line. A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface.  
Seemingly complex forms can be built by ruled surfaces. Ruled surfaces are formed when one curve is extruded along another curve. Hence by changing the parameters of these two curves many forms can be achieved.
Inspired from traditional coconut leaflet weaving , this base surface is reconstructed from a diagrid timber knitting. <p>
For the manufacturing of this a steam bend approach is to be done. The knit pattern is defined as completely of timber strips and as another option with timber strips as the main grid and a secondary structural grid made of steel members.


The system is considered to be site less and can be deployed in any site based on different functions. But the climate chosen for the design is the tropical warm and humid climate of Mumbai.
For the next step of development the base unit is optimized using evolutionary solver called wallecei. The optimization is based on three criteria: Fitness Objective 1 : Minimizing the displacement for the overall shell of the structure.
Fitness Objective 2 : Maximizing the shadow cast by the structure on the ground. For this a mean sun path position is extracted for the site using ladybug analysis.
Fitness Objective 3 : Minimizing the overall volume of the structure and keeping the center of the structure close to the original boundary set. The optimization was ran for a population of 10000 individuals along 5 generations.
Out of these iterations three were chosen as the final selections based on a balanced result values for each crieteria. From this a best performing option was selected.
The next step was to create a more balanced and stable structure by using the base units. So an approach of symmetry and repetition can bring in more stability as the interconnections increase. Based on structural analysis, an optimal orientation of structures was found.
Columns supporting these interconnection were added for additional stability. These columns were then reimagined as an extension of the modules interconnecting and merging into the ground.
This interconnected from is then optimized further based on stability and volume. and the final set of iteration was derived from which the the best performing induvial would become the final design form. These forms integrated landscape features into it creating an optimized output that functions well with the surroundings and activities.
The final best performing solution is selected considering aesthetic and functional qualities as well.


The next stage was to figure out the fabrication process and a series of prototypes for constructing one module was done . The first porotype involved generating a frame of the ruled surface.
This framed form which created the ruled surface was studied based on the possibility of bending strips in place and assembling them together. But the initial model informed us that the framed system itself hinders the process of interconnection of the timber strips.
For the next study model the base ruled surface is created and this surface is then used to assemble strips extracted from the final from using grasshopper. This helped in achieving the desired form and bending. But this approach had many disadvantages as the initial surface creation in actual scale would increase the cost of construction and the wastage of material will be higher.


Based on the study models a truss assembly approach for fabrication was adopted. The individual timber strips extracted from the final form is bend individually in a bending formwork and these bend timber strips are connected in pairs using steel brackets. These paired timber strips forms a truss and this is then assembled together.
For this approach form work for bending each timber strip is extracted and the angles and position of each member of the form work is extracted from grasshopper.