Research

The practical geometry of the ancient Egyptian “rope-stretchers” delineated land after the annual flooding of the Nile River. Thus, the term “geometry” derives from the Greek words “gaia” (earth) and “metria” (measurement). Greek mathematicians used compass and straightedge to perform similar calculations on paper. This…

A spiral is a curve that begins at a central point and continuously moves outward, either getting larger (in an outward spiral) or smaller (in an inward spiral). It often revolves around a central point or axis. Spirals are fascinating because they appear in many…

A fractal is a complex geometric shape that we can split into parts, each of which is a reduced-scale copy of the whole. This property is self-similarity. Fractals often exhibit patterns that repeat at different scales. We can find fractals in nature, such as in…

In mathematics, “curve” describes one-dimensional objects or line shapes, regardless of their curvature. Straight lines, polylines, and curved lines all fall under the category of “curves.” You may remember working with equation graphs in high school math classes. For instance, a first-degree equation produces straight-line…

The Flowsnake, or Gosper curve is a space-filling fractal. It is also known as the Peano-Gosper curve. There are other similar space-filling fractals such as the Dragon curve, or the Hilbert curve. A space-filling fractal is a special type of curve, that fills a plane…

In computer-aided design (CAD), a polyline is a series (or a chain) of straight lines. Each straight section of a polyline is a “segment,” and the points where the segments connect are “vertices.” If a polyline’s starting and ending vertices coincide, it is a “closed…

Below is the first paper of my son, Mete Yazar. It is about a mathematical and geometric exercise of calculating the surface area of an arbitrary shape (a classical guitar’s body panel). He did a good job in utilizing Bezier/de Casteljau curves and generating the…

ASCII art is a graphic design technique that uses characters from the ASCII (American Standard Code for Information Interchange) set to create images, symbols, and designs. This form of art involves arranging text characters to form a visual representation of objects, scenes, or abstract patterns….

Holger Strøm designed the famous IQlight system in 1973. After more than 50 years, it is still a popular, innovative, and smart design. The IQlight is a self-assembly lamp composed of interlocking quadrilaterals. By utilizing polyhedral geometry, you can generate various shapes and sizes. I…

In architectural research, a significant challenge in robotic fabrication is replicating setups due to the unique configurations used in each study. There is a lack of a unified software platform connecting various researchers and their robotic setups. Additionally, the fabrication tools are typically not open-source…

A pendentive is an architectural feature used in domed structures. It is a triangular section of a sphere that allows for the transition from a square or polygonal base to a circular or polygonal dome. Pendentives curve upward from the corners of the base and…

This is the latest reel video of the Online Virtual Studio (OVS) project. We conducted it together with Oğulcan Üneşi and Serkan Uysal since 2022. We tried to develop a tool for online and blended education in architectural studios. The tool has specific features tailored…

Here is the shortest possible way of generating quick parametric curves in Rhino Python. So, you may change the f, g, and h functions to test any function curve. In this Python code, the list comprehension [(f(t), g(t), h(t)) for t in [t0 + i*dt…

Modeling a rhombicosidodecahedron requires exploding and extending the faces of a dodecahedron and an icosahedron of the same edge length. We begin with both polyhedra centered at the same point. Then, we explode the faces of the dodecahedron and icosahedron outward from the center. We…

Today’s polyhedra are the famous Archimedean Solids! I created a simple Grasshopper script to generate pendants from these beautiful solids. I call this Archimedean Pendants. However, you can implement other polyhedra to the same code. I hardcoded the vertex coordinates so you won’t need an…

Urban Atölye, led by architect Nilüfer Kozikoğlu initiated the development of this Grasshopper code. The concept was to create a random relief pattern on a surface to be carved out using CNC technology. In Turkish, this technique is referred to as “kaşıklama,” as the resulting…

The Image Sampler has always been a very effective Grasshopper component. Once again, I had the opportunity to use this component for a professional job. As you can see, with the help of a straightforward and short script, we can create a relief of an…

Here is a wave generator code I developed using Grasshopper and Python. While searching for a solution to the realistic water simulations, I came up with the Gerstner Waves. I tried to implement it. However, I came up with this final result, which is not…

A Penrose tiling exemplifies a type of tiling known as aperiodic. In this context, tiling involves covering a plane with non-overlapping polygons or shapes. Aperiodic means the tiling lacks arbitrarily large repeating sections. These tilings derive their name from mathematician and physicist Roger Penrose, who…

It is not possible to cover a double curvature surface with planar quads. Here is one method that overcomes quad tiling on double curvature by pulling one vertex of the quads to the plane defined by the other three. This method was used in architecture…