In this short tutorial, I am showing the essentials of data domains in Grasshopper. A domain is a data type in Grasshopper that represents a portion of the 1d or 2d number space. This requires a starting and ending point in those spaces. In 1d, these points are two numbers. Then, the domain represents all the numbers between them. In 2d, a data domain is represented by two coordinates (u, […]

In 1986, Craig Reynolds developed an algorithm aiming to model the flocking behavior of birds, which remains a cult method used in flock simulations today. In my initial study, the bird-oids (boids) have no rules or limitations, just chilling randomly on the screen. I call this initial version Wandering Simulator. There are several reasons why this fundamental simulation is difficult in Grasshopper and Python, our parametric design interface. In Grasshopper […]

Here is a method for coding the dodecahedron and all its irregular variants in Grasshopper as quickly as possible. I utilized the golden ratio rectangles, usually used to construct the sister polyhedron, the icosahedron. However, the magic component of the Grasshopper, the Faceted Dome rescued me again to generate the dual of it, the dodecahedron. This is a special platonic solid, which has 12 regular pentagonal faces. There are several […]

This is the new version of my previous study on the deformation of Islamic Patterns. I love the purity and simplicity of the geometric construction processes of these patterns. It is possible to observe them in many places in many different forms. By continuing this work, I aimed to highlight the pattern deformations that map out all the variation possibilities of these patterns. Unlike previous versions, this time I aimed […]

This is the continuation of my previous study on the Fibonacci lattice on a spherical surface, creating a Fibonacci Dome structure. The panelization of curved forms with flat surfaces has been a favorite topic in architectural geometry. The trigonometric layout of the Fibonacci sequence generates a spherical formation, while the Faceted Dome component handles planarity. Here, I further enhanced the previous code into a pavilion design. The essential part of the […]

This work emerged out of necessity. In the design and application process of wooden frame structures, where we put thousands of pieces together like a puzzle, the issue of preparing and updating quantity and measurement lists requires the most effort. Hours spent on this and the possibility of making mistakes are very high. However, with the Quantity Surveyor I developed in Grasshopper, you can generate measurement lists almost in real-time. […]

The regular dodecahedron is one of the five Platonic solids, characterized by having 12 regular pentagonal faces, 20 vertices, and 30 edges. When you elongate it, you extend its structure in one or more directions, resulting in a shape that retains the basic properties of the dodecahedron but is stretched out. The elongated dodecahedron might not catch your eye at first—it’s just a long version of a shape you’ve probably […]

Today’s computational curve is the beautiful Sierpinski Triangle. It is a fractal named after the Polish mathematician Waclaw Sierpinski, who described it in 1915, though it had been previously described by other mathematicians. It is a self-replicating pattern that arises from a simple recursive process. To construct the fractal, you start with an equilateral triangle and then repeatedly remove smaller equilateral triangles from its interior, leaving holes. Each iteration involves […]

The rhombic dodecahedron is a polyhedron with twelve rhombus-shaped faces, where each face has four sides of equal length. It is possible to construct the space-filling variant of the rhombic dodecahedron by arranging multiple such rhombic dodecahedra in a regular pattern so that they fill space without leaving any gaps. In his 1611 work on snowflakes titled “Strena seu de Nive Sexangula,” Johannes Kepler observed that honey bees utilize the […]

Lissajous curves, named after the French physicist Jules Antoine Lissajous are a family of curves that emerge from the interaction between two harmonic oscillations. They have applications in various fields including physics, engineering, and signal processing. They are commonly used in electronic devices such as oscilloscopes to visualize the phase relationship between two oscillating signals. Similarly, they are also useful in mechanical engineering for analyzing and designing mechanisms that involve […]

Geodesic refers to the shortest path between two points on a curved surface. It is based on the principles of geodesy, which is the science of measuring the Earth’s shape. On the other hand, in architecture and design, a geodesic dome is a spherical or hemispherical structure consisting of a network of geodesic lines (great-circle arcs) forming triangles. Therefore, the dome’s framework provides strength and stability, distributing stress throughout its […]

Stellated polyhedra are three-dimensional geometric shapes formed by extending the faces of a regular polyhedron (a solid with flat faces) beyond their original boundaries until they intersect with each other. The term “stellate” comes from the Latin word “stella,” meaning star and these polyhedra often have a star-like appearance due to their extended faces. They are popular because of their aesthetic qualities. I studied these forms many times before. This […]

In 2016, archi-union architects and fab-union intelligent engineering completed the renovation of the art gallery in Shanghai, China. The distinctive feature of the building was the robotic masonry fabrication of the brick facades. The undulating and waving parametric bricks were increasingly becoming popular after the introduction of parametric design tools such as Grasshopper and the works of Gramazio & Kohler at ETH Zurich since 2008, I guess. I made two […]

Catalan Solids are the duals of Archimedean Solids. They were first described by mathematician Eugène Charles Catalan in the 19th century. There are 13 Catalan solids, and they exhibit interesting symmetries and unique characteristics. While coding the vertex coordinates of these solids in Grasshopper, I made a simple lamp design to exercise the programming language. The code generates the 13 Catalan Lamps with flaps. Since the polyhedra have planar faces, […]

While reviewing past Grasshopper studies, I stumbled upon a Parametric Muqarnas study dating back 11 years. Although it shares numerous characteristics with a muqarnas design, it is not a perfect match. The Grasshopper definition used in that study was not particularly efficient, prompting me to revisit and improve it. This particular design presents various challenges, making it an excellent exercise for mastering Grasshopper. My goal with this study was to […]

The interlocking frame structures represent a quintessential example of parametric design since very old times. More recently, they gained widespread attention through the Metropol Parasol in Seville, captivating architects and designers. I’ve extensively explored these structures on this blog, attempting various methods like manual slit drawing and solid/region boolean operations. My latest iteration aimed for greater simplicity and adaptability on complex surfaces. I call this new version Interlocking Pavilion. The […]

Archimedean Solids are convex polyhedra with faces of regular polygons and vertex-transitive. There are 13 such objects (excluding prisms and antiprisms which are probably less exciting). In this study, I experimented with these solids and designed a family of planters. Since they are convex and look cool, I decided to give it a try. I call this algorithm Archimedean Planters. The first part of the definition deals with the generation […]

“In the heart of a sunflower’s embrace, its seeds weave a poetic tale—a dance of two spirals, parastichies they’re called. One unfurls gracefully from the center in the hush of clockwise whispers, while its counterpart whispers secrets in the tender breaths of counterclockwise motion. A subtle ballet unfolds, where the number of these spirals gracefully mirrors the whispers of adjacent Fibonacci numbers, composing a delicate symphony in the sun-kissed fields.” […]

Today’s curve is the beautiful Bezier curve. A series of linear interpolations between the coordinates of control points describe a Bezier curve. So, I created a simple tool in Grasshopper called Bezier Function Extractor to experiment with this elegant construction. In the linear form (degree 1) the linear interpolation between 2 points (P1 and P2). The point at parameter t (0<= t <= 1); Q = tP1 + (1-t)P2. In […]

This week’s fractal is the famous Dragon Curve. Dragon Curve exhibits self-similarity, meaning parts of the curve resemble the overall shape, regardless of scale. It’s fascinating because a relatively simple construction process generates a complex and visually captivating fractal pattern. The Dragon Curve is often used to demonstrate fractal properties in mathematics and is popular in recreational mathematics due to its intricate and beautiful patterns. It has applications in computer […]