I’ve been searching for a method to study the Voronoi subdivision in order to manipulate it. There are well-known algorithms for that. But I thought it would be better if I use a projective approach just as I did in studying hyperbolic space (here). This is the metaphor of inflating balloons. However, I inflated cones instead of spheres. This way, it became possible to modify the algorithm. So I was […]
Today’s Architectural Geometry course was about platonic solids and different attractor objects in introducing component-based design systems. Benay’s idea was both pedagogical and interesting to test in Grasshopper. I searched for the most fundamental type of attractor solid in creating a composition such as this; There is a subdivided sphere and an attractor sphere. The pull component works great here. You may use multiple attractor solids or different shapes such […]
In this exercise, we asked students to develop a method to produce custom tessellations. This is based on the analysis of what is called “Islamic patterns”. We have discussed Eric Brough‘s famous book “Islamic Geometric Patterns”, regarding geometric relationships and linear connectivities via underlying tessellations (such as regular square and hexagonal). Thus, this geometry and drawing exercise is called “Seamless Patterns” in the Design Geometry course at İstanbul Bilgi University. […]
The first-year Architectural Geometry course includes Euclidean constructions as a study of associative geometry. We have exercised the below questions to study this topic. These are three mutually tangent circles, that can be drawn using only a compass and ruler, without built-in tangency functions in Rhino. Such exercises are expected to improve students’ reasoning. We believe architectural geometry education should encourage a conception that allows students to think about what […]
This is my first try at DesignScript syntax. It is quite easy to understand and on-screen reference help seems to work well. It creates regular AutoCAD entities when you run. One of the most important concepts of this language is said to be a kind of associativity that updates objects when any parameter is changed while the script is running. However such associativity is not possible after the script has […]
Last week, the first-year architectural geometry course was about pattern deformations. Students are expected to familiarize themselves with 2d drawing, transformation, and control point editing commands while trying to design a deformation. After studying regular and semi-regular tessellations of the plane, they are expected to develop reasoning on the rule-based and iterative processes. This also constructed an underpinning for Basic Design‘s “Metamorphosis” study, where they have discussed more conceptual frameworks […]
The Möbius strip is a famous mathematical object. Although being in three-dimensional space, it is a closed-loop of only one surface and only one edge. This quality alone makes the object an interesting study for computational design. I aimed to create an object to test our new CNC machine. I wanted to test the egg-crate interlocking fabrication method. This is why the study became a Möbius strip fabrication. Apart from […]
This is not to explain the method of the Parquet Deformation but to see the potential. After we’ve studied regular, semi-regular, dual, and truncated tessellations with students, the Architectural Geometry course expects them to develop a Parquet Deformation handmade such as those shown below. I call them Parquet Deformation handmade. Because they are manually designed but drawn using traditional CAD. The samples you see below are from this website. It […]
Nowadays I plan to enter Rhinoscript, Python, and DesignScript back again. However, I can’t leave Grasshopper3D without mentioning the “cognitive shift” it pioneered in the design computing community. Here is a phrase from a famous special issue of “Computer” Journal, published in 1982 with Tilak Agerwala and Arvind’s editorials; Data flow languages form a subclass of the languages which are based primarily upon function application (i.e., applicative languages). By data […]
This is a late update for my 2012 study on Cairo Pentagonal Tiling (or Cairo Tessellation). Originally, it was an exercise of dual tessellations. Because this tiling is the dual of the famous semi-regular tessellation of Snub Square. After coding the Snub Square tiling, I attempted to generate the dual of it. However, that created an inefficient result. This latest version generates the original Snub Square and Cario Pentagonal Tilings. […]
This was the first step in the generation of Cairo Pentagonal Tiling. It is the dual of a semi-regular tiling of the snub square. The first step was easy. Just dispatch cells of a square grid, then evaluate them according to the ratio of 0.366 approx. which is derived from the bisector of an equilateral triangle. Here is the definition: [GHX: 0.9.0014] Now, we have a snub square tiling, composed of […]
The intricate harmony of the Islamic Patterns is amazing. The geometry of this and other Islamic pattern designs are explained in the 3rd chapter of Craig S. Kaplan’s Ph.D. dissertation. I constructed a semi-regular tessellation, particularly the 4.8 because it seems to open interesting explorations that mostly emerge from truncated squares. We know equilateral triangles and hexagons are also fundamental shapes for this task. However, the dual nature of the […]
In 1982, it has been more than 15 years since the dataflow approach to algorithm designing are discussed in computer science. Computer journal publishes a special issue with the foreword of Tilak Agerwala; he says; …We have discussed two characteristics of the von Neumann model of computation: global updatable memory and a single program counter. It will become clear shortly that the data flow model has neither of these. First, the data flow model […]
This was my old plan to work with images in Grasshopper. Certainly, that was not the result I expected, but this could be counted as a starting point. After seeing beautiful circle packing compositions here, I decided to program Grasshopper, so that it’ll create a subdivision, based on image data. This was the initial version, just subdividing a plane with Voronoi points and visualizing it according to the image’s color […]
Mandelbrot set is the continuation of a previous study on Julia sets (studied here). According to this website: The Mandelbrot set, named after Benoit Mandelbrot, is a fractal. Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely […]
Today’s fractal is the Julia Set, the amazing simplicity of chaos. There are lots of applets and articles on the internet about this fractal. You can generate this with the iteration of a basic function many times and placing points on the complex plane. I developed a Grasshopper implementation in 2012. Also, this was my first study on complex numbers. At each iteration, the detail level increases. I utilized a […]
Studying circle packing led me back to my high school days. First, I’ve tried to write a vb.net component so that I would say Grasshopper to place circles and check lots of things iterating again and again. Then I felt that this was not my real interest in circle packing. After finding an old post by Daniel Piker (here), I’m truly enlightened about an old topic of our high school […]