The term “hexa” generally refers to the number six, derived from the Greek word. It is commonly used in mathematics, geometry, and other scientific fields to indicate six-sided shapes or structures. A hexagon is a polygon with six sides and six angles. It is one of the regular polygons, meaning all of its sides and angles are equal. A hexahedron is a polyhedron with six faces. The most well-known example […]

The Koch pentagon is a fractal shape that starts with a regular pentagon. Here, we divide each side of the pentagon into three equal parts. Then, we replace the middle with two sides of an outward-pointing equilateral triangle. We repeat this process for every new side in each iteration, creating a self-similar pattern. Helge von Koch (1870–1924) was a Swedish mathematician known for his analysis and number theory work. He […]

In geometry, “tangent” refers to a scenario where a line, curve, or surface touches another at exactly one point without crossing or leaving a gap. A tangent line to a circle is a straight line that touches the circle at only one point, and it is perpendicular to the radius at that point. Two circles can be tangent either internally or externally. Geometric constructions using a compass and straightedge can […]

The geometric shapes constructed using only a compass and straightedge have significantly influenced the development of reasoning and logic that underpin modern science. This non-numerical approach is also known as the Synthetic Geometry. Before René Descartes introduced Analytic Geometry, this method was widely studied and practiced. In “Elements”, Euclid explores fundamental rules, such as ‘The straight line between two points is the shortest,’ and derives all geometric truths from simple, […]

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 abstract thinking allowed for insights into the underlying logic, independent of the accuracy of hand tools. So, the abstract “circle” and “line” constructed by perfect […]

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 aspects of nature, mathematics, and art. In this drawing exercise, I utilized several commands to draw such a system. However, this drawing is not a […]

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 snowflakes, mountain ranges, trees, and clouds. We can also generate them mathematically. Fractals have applications in various fields such as physics, biology, and computer graphics. […]

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 graphs, while higher-degree equations, like “x squared,” create curved graphs. In this context, we focus on degree-1 curves, drawing straight-line segments using the polyline command. […]

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 when iterated infinitely. This means, that if you continue to replace every segment of the polyline with the whole drawing, it will quickly become very […]

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 polyline” or a “polygon”. If they do not, the polyline is classified as an “open polyline.” Polylines can be planar (2D) or 3D. The Gosper […]

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. I first encountered this art form in the 90s through readme text files and computer games. Years later, attempting to automate it in Grasshopper was […]

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 created a model of one of the most common IQlight designs, fitting it onto the Catalan solid known as the rhombic triacontahedron. This solid is […]

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 support the dome above. They help distribute the dome’s weight more evenly and enable the construction of a dome over a non-circular base. I created […]

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 for design studios. İstanbul Bilgi University Scientific Research Fund partially supported this project. This video showcases the latest toolset OVS provided. The tool takes some […]

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 for i in range(int((t1-t0)/dt)+1)]] works by first generating a list of t values from t0 to t1 with an increment of dt using the inner […]

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 extend their planes while maintaining their orientation and shape. As these faces extend, they intersect and form new polygonal regions. Triangular and pentagonal faces emerge […]

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 extra add-on to generate the polyhedra. Thanks to the new SubD component Multipipe, it makes life much easier to produce 3dprint-ready results. To make this […]

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 shapes resemble those carved out by a spoon. Consequently, I named this Grasshopper definition “spooning.” The definition employs the Populate Geometry component to achieve a […]

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 image to fit the desired panel dimensions on the screen. We can process this onto a suitable material using a CNC mill, laser cutter, or […]

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 Gerstner Wave generator, but a much simpler one. It combines many user-fed wave components and calculates the resulting single wave. I played with this […]