Tessellations

An aperiodic tiling is a pattern that covers the plane without ever repeating itself (i.e., it is non-periodic). A few special shapes, arranged according to specific rules, can cover the entire plane, but the resulting pattern never repeats exactly. I challenged myself on a 3-day…

In large-scale projects, calculating tiling layouts for wall, floor, and ceiling surfaces becomes even more critical. Evolutionary optimization of these tilings seemed to be a viable approach yesterday. Considering how time-consuming and labor-intensive this process can be, I tried using Galapagos, an old but often…

Although it appears simple, Goldberg Polyhedra in Grasshopper became a tough challenge, which I like a lot. I spent about 24 hours attempting to generate these polyhedra. I started with Goldberg’s original method. This creates an equilateral triangle using coordinates denoted as m and n…

Snub Square Tiling is a semi-regular tessellation of the plane, composed of two squares and three regular triangles at each vertex. The arrangement of these two regular shapes seamlessly covers the plane without any gaps or overlaps. It is one of the eight semi-regular tessellations…

In Japanese, “kagome” refers to basket weaving, and the name of this tiling derives from the traditional basket-weaving craft of Japanese culture. In geometry, we know Kagome tiling as a semi-regular tessellation, Tri-Hexagonal Tiling. This tiling is composed of regular hexagons and triangles that cover…

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…

The rhombitrihexagonal tiling is one of the semi-regular tessellations. It is composed of regular hexagons, squares, and triangles. It is a periodic tessellation since you can copy the fundamental unit and move it across the plane to generate the tiling. I use this quality of…

The snub square tiling is one of the semi-regular tessellations, where regular triangles and squares match perfectly to fill the plane without gaps or overlaps. The Euclidean construction of Snub Square tiling is possible by utilizing the basic compass and straightedge operations. I made this…

“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…

This is an update on my 2012 exercise on rhombille tiling. This reminded me of the old-school subdivisions of surfaces again after 11 years. It was while reading about rhombic dodecahedron (the stackable solid), that I came across this cute tiling. It’s quite simple, just…

This is the six-pointed star lattice definition in Grasshopper. The definition is generating CNC or laser-ready results as seen below. In this code, first, I developed a common star pattern by exploding a hexagonal grid. The tricky part of this definition is the last part….

In this Voronoi puzzle exercise, we derive two-dimensional puzzles by using Voronoi diagrams. This is similar to my previous studies here, and here. Part 1: The Random Voronoi Diagram In section 1 of the below image, I use a rectangular region to generate random points….

This python code proves how much effort it takes to create a simple hexagonal tessellation. There are, of course, much easier and faster methods than this. But here you see a code that introduces students to Rhino Python. Using this code, a new Rhino command…

Further studying iteration in Grasshopper, this time, inspired by George Stiny’s “Chinese Ice-Ray Lattice” subdivisions with Aneome, instead of the Hoopsnake add-on I tried in the previous work. As you know, loops add various ways of usage to Grasshopper. In future versions, loops may cease…

This quick project was about a special tiling pattern inside a multi-story residential building’s hallways in Grasshopper. While drawing the construction documents of the project, it was necessary to apply some coding here, as each floor had a different shape to be tiled. Although it is not…

Again, we revisited the seamless patterns exercise this semester. This is one of the main exercises of architectural geometry class. We expected to improve students reasoning on generative patterning while they explain their processes step by step. The key element of this exercise is the usage of…

This is one of the ideas we’ve tested for the workshop “Animate Patterning“. Inspired by this work, Apart from the pattern that turns around, the torque, rotation radius and speed of the servo, weight, connection detail, and a number of foamboards become important inputs for…

I’ve come across this nice website about the short history of tilings and tessellations. In this post, I am regenerating a tiling of Dürer rhombii. Albrecht Dürer sounds like one of the pioneers of some of the concepts of today’s emerging field of architectural geometry….

Recently, I returned to old fashion RhinoScripts in order to recapture its idea and functionalities again. After almost 10 years, this is my first experiment on creating a custom function that draws hexagonal grids. I tried to implement a fast process for it, however, there…

Kündekâri is an old woodworking technique, composed of interlocking parts without any glue or nail. It is primarily used in wooden doors and minbers inside Mosques. The interlocking system makes the whole structure very durable. I tried to model this technique using the Voronoi pattern,…