Algorithms

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 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…

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…

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 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…

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….

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…

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…

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…

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…

De Boor’s algorithm, a maestro of basis spline refinement, meticulously navigates through knots, unraveling the intricacies of B-splines with mathematical precision. Meanwhile, De Casteljau, the geometric orchestrator, takes center stage in the Bezier ballet, elegantly guiding control points through a recursive dance. Together, these algorithms…

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…

The Hilbert Curve, also referred to as the Hilbert space-filling curve, was initially introduced by the German mathematician David Hilbert in 1891. It is a continuous fractal curve, presenting a variation of the space-filling Peano curves uncovered by Giuseppe Peano in 1890. After a study…

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…

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…

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…

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…

“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…

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…

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…