Week 4: Geometric explorations part 2

Previously, I have looked into computational manipulations based on the frame of the Armenian stone carving patterns, in particular, the work on the Geghard monastery dome, which is a great example of the Armenian stone masonry style of 5th century.

From 2D to 3D explorations of the stone masonry specimen

I have conducted further preliminary studies in pattern recognition, sectioning and tessellation. Modern maths is described as a science of patterns, hence the mathematician analyses patterns which can be geometric, numerical, visual or mental, static or dynamic etc. These patterns can derive from nature, or can be arrived from within inner workings of human brain, as well as they can be generated computationally.
I will be looking into the intersection of the visual, analogue geometric patterns and the ones that have been assembled through following design algorithms, which, nevertheless, bare reminiscences of the analogue framework.

Geghard dome single pattern expansion

According to Stanford university professor Keith Devlin (http://www.stanford.edu/~kdevlin/), arithmetic and number theories deal with patterns of counting and numbers, calculus portrays patterns of motion, theory of probability studies patterns of chance, logic is an exploration of patterns of reasoning, geometry investigates shape patterns, topology looks into patterns of closeness and position and fractal geometry unveils the self-similarity patterns found in the natural world. These last three mathematical applications are the ones I will be using most frequently in my explorations. 

Topology pattern studies

The main 3D software tool I have at my disposal has the above mathematical concepts already embedded in its platform, so the manipulations of the shape and topology produce the mathematical results, as shown on the above example. Here, the hexagonal seed structure, was populated to form a continuous mesh and in essence became the building block of the surface, hence the change of the parameters of strength and growth iterations on the seed are translated onto the whole fabric.

Tessellation as topology determinant

In its most basic form, tessellation is simply a method of breaking down the polygons. The analogue concept of tessellation is that of a seamless tiling of shapes that create a continuous surface. Digital tessellation merges these concepts and when aligned with other algorithms of mapping and displacement, produces extremely high resolution geometries. On the above example, the seed building block is tessellated on 2D plane, thus changing the resolution of the outcome.

Topology tessellation and shape manipulation

3D tessellation is programmable and it opens the doors to enormous potential to new design frontiers. On the last example, the topological tessellation enables much complex shape deformations.  Next I will be looking into the application of these studies in parametric architecture and scripting.

Parametric manipulation of sections

In the example above, the reference stack of planes (light orange) is "remotely" manipulated with the 3D shape (in grey), which itself, however, is absent from the final design, still, the sections describe the shape through the negative space. Each geometric change in the original shape is instantly resonated in the final output. These and other parametric relationships present intriguing possibilities for modern architects.

Parametric manipulations of 3D shapes

Parametric architecture is a liquid discipline that has evolved rapidly during the last 3-5 years, offering curious, speculative and experimental design scripting. My intuitive approach is to start direct manipulations of the above discussed techniques on the past methodology of stone carving and perhaps some unpredictable outcomes will materials themselves.