The development of geometry began by measuring the world as discrete objects. Moving beyond measuring nature, it evolved into reasoning, calculation, and mathematics. Platonic solids were one of the most elegant and beautiful ideas reached by geometry. Pondering why there are only five of them was a tribute to collective human intelligence. Earlier in this blog, we modeled polyhedra, like the Platonic solids, using geometric construction methods. This process was like solving a puzzle. To construct a point whose distances…

Last year, during the first stage of the Architectural Design Graduate project, our student team made a quick preparation and participated in the experimental works exhibition at the International Antalya Architecture Biennale (IABA 2025). This was a challenging yet educational process for our team. Using EPS foam and the robotic hotwire cutter (RHWC), a production run of 125 units, consisting of two modules (95 octahedra and 30 icosahedral units), was carried out. The icosahedral units also underwent an additional cutting…

While trying to program the curves produced by Spirograph toys in Grasshopper, I took a slightly different path. The topic eventually led to a broader heading: harmonic motion, and from there, to the Fourier Series we looked at previously. This simple Python code models Fourier Synthesis, driven by circles of different radii in a very straightforward way. The Python component sets up a loop that calculates the effect of each circle to the x and y values, individually. In this…

In his groundbreaking 1935 text ‘The Work of Art in the Age of Mechanical Reproduction,‘ Walter Benjamin questioned how photography and cinema radically transformed the nature of art. According to him, what made a work of art unique was its singular existence in time and space, its ‘aura’. Mechanical reproduction techniques shook this aura, detaching the work from its traditional context and offering it up for mass consumption. Today, we stand at a completely different threshold. Generative AI tools are…

This is the last of the site analysis tools we previously used in first-year architecture education. As you may recall, we previously introduced a tool that generates topographies based on specific parameters. Afterward, we examined two tools that perform slope and flow analyses on these topographies. Today, we are presenting a tool that analyzes curvature. This topic actually constitutes one of the interesting intersection points between architectural design and differential geometry. Curvature is not something architects normally observe directly on…

This project randomly stole an entire evening of mine. I didn’t know what the cantellation operation was. After doing some research, I realized it mirrors the process of the dual operation we had previously performed with polyhedra. It turns out to be the process of turning edges into new faces. I started looking for ways to do this in Grasshopper without using ready-made add-ons that include this and similar operations. As always, I had to solve many interesting geometry and…

For a research project with Avşar Gürpınar in 2024, we studied lace patterns. During this process, I had the opportunity to try out two Grasshopper plugins: Parakeet and Clipper. When combined, they allow you to obtain laser-cutting patterns. Parakeet is a very good plugin that generates tessellations. This was something I always dreamed of developing back in my youth. 2-Uniform Tiling In this design, I used the Parakeet component named 2-Uniform Tiling. In geometry and tiling theory, a 2-uniform tiling…

I’d like to write down an interesting problem here. I remembered this while thinking about this post. It represents one of my favorite, simple pieces of reasoning. I frequently find myself needing to sort a number of points around a center in Grasshopper. Don’t ask why. I realized I’ve been using three different methods to achieve this. The first one that comes to mind is using the Vector Angle component, naturally. All we have to do is supply a plane…

Hot-wire cutting (HWC) is a cost-effective subtractive fabrication technique used across many industries. The basic idea of HWC is to cut a block of material by melting it with a resistance-heated wire under tension. It is effective for materials with low melting temperatures, such as expanded polystyrene (EPS) and extruded polystyrene (XPS). Generally, HWC is associated with mold production in the architecture, engineering, and construction (AEC) industries. Robotic hot-wire cutting (RHWC) is a subtopic of HWC. In a standard RHWC…

We previously looked at the terrain generator script we used in projects with first-year architecture students over here. Later on, we added a few analysis modules to this tool. You might remember the slope analysis tool from this link. Today’s topic is another type of analysis: flow. The idea for this code wasn’t actually mine; I developed it by looking at an existing script based on Serkan Uysal’s suggestion. Unfortunately, I don’t know who originally wrote it. Keeping track of…