#tessellation

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 construction in Rhinoceros to show that there is no need for any numerical input to locate the points and draw the tiling. There are two major techniques explained there. One of them is the basic…

Here are the variations of classical six-pointed star patterns generated by Grasshopper. Generally, you can see these patterns under the title “Islamic patterns” because they are frequent in the decorations of mosques and palaces. I studied these patterns in Grasshopper earlier in these posts. I always find this an interesting geometry exercise. This time, my main goal was to develop a useful code only with the native Grasshopper components that create laser-cut-ready products of hexagonal star lattice. Thus, I made…

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. There, you can see how you can use the Region Union (RUnion) component to add thickness to a pattern we have drawn before. The operation here will require trimming and extending commands under normal conditions….

Here is one of the exercises I tested with a few students in Architectural Geometry. The exercise is about creating Escher-like patterns. It is an introductory topic on the designerly utilization of regular tessellations. We use square, hexagonal, or triangular tessellations as underlying structures of complex patterns. Below are some of the student works from this exercise. I think the black-and-white coloring helps in terms of reducing the requirements. Although the patterns designed in this exercise are not Escher patterns,…

This is one of the ideas we’ve tested for the workshop “Animate Patterning“. 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 this design. In the three-day workshop, one group of students interpreted this idea of using several moving layers and creating an emergent pattern at the perceptual level. However their project was slightly different from this one, I’ll post their…

Basic Design I exercise called “Cut and Fold: Deviation” explores diversity within relationships and material behavior. It is initially introduced by Salih Küçüktuna as a simple but effective exercise platform. Below are some students’ works on this one-week exercise. The term “deviation” has many uses in a range of fields from medicine to sociology. However, it is frequently used in statistics with an interesting evocation to design computing: In mathematics and statistics, deviation is a measure of difference between the…

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. Here is a phrase from that website about Dürer; “…Like Kepler, regular polygons and polyhedra fascinated Dürer… A large section of the Painter’s Manual is dedicated to practical ways to construct various curves and regular polygons with…

The Parquet Deformation exercise is generally originated with William Huff. Huff conducted it at several schools of architecture since the 1960s. Huff defines the exercise as rooted in two analytical disciplines; monohedral tilings in geometry, and the continuous deformations in biological morphology. This is generally exemplified by D’Arcy Thompson’s and Albrecht Dürer’s studies. One of the student’s works of Huff, Trifoliolate is a single-axis, single-prototile hexagonal parquet deformation. It was designed by Glen Paris at the studio of William Huff…

For the last 10 days, I’ve been searching for a proper algorithm for representing surfaces using planar shapes. It is obvious that triangulation is an answer but there is an interesting research topic of planar remeshing using shapes other than quads, hexagons, or any other regular polygons. Especially in computer graphics, such things refer to the optimization of models to decrease the load of GPUs. In the Grasshopper community, this has also been discussed and there is a great implementation…

It all started with my new passion for origami tessellations, not much of origami, but the tessellation part. I was too lazy to fold it physically, nor model them using an engine such as Kangaroo. That would also be very unnecessary (and yes, very boring) to simulate a folding effort on the computer unless we lose our connection with the real world. Instead, I tried to look at a much more abstract, silly, and basic part of it; the creasing…