This is another popular “math surface” being rediscovered by designers nowadays, in 2012. Saddle surfaces, seen above as mentioned earlier (here) have a special type named “Monkey Saddle Surface”. This surface was a dramatic example of how Grasshopper can control equations and instantly show graphical results. The mathematical equations start with Z=… this makes it very easy for us to transform any x-y grid centers (a 2d data tree of […]

After Puzzling, I tried to establish more of Escher’s basic grid transformations using Grasshopper’s native components. This definition simulates Escher’s transformation of four-cornered grids. The postulate is based on the fact that every quadrilateral (or triangular) planar shape can create regular tessellations without gaps or overlaps. In the traditional method, this tessellation is achieved by rotating the shape 180 degrees and copying afterward. However, in Grasshopper we simply define the […]

Nowadays, I found myself back into traditional hand sketching. Several failed attempts on Grasshopper led me back there. NURBS (and Grasshopper) somehow limits our conception of surfaces to four-cornered (or two-directional) manifolds. Although it sounds like limiting our designs, having four-cornered component spaces has still lots of experimental fields for designers. Escher is a cult person, who transforms the euclidean coordinate system to meet his design intentions. There are lots […]

This topic of trees and recursive computing is inspired by the method shown here at the Rhino Python 101 Primer. This is a beautiful method of recursion that creates tree-like shapes, composed of arcs. I constructed these arcs by using the Arc SED (start, end, direction) method. This requires start and end points and a vector that is tangent to the arc (at the start point). Therefore, the overall look […]

Today, we’ve discussed ways of subdividing entities to create parametric definitions. Curves can be divided into segments, creating snake-like object definitions. This exercise is important regarding the management of data. Vectors and planes are used as reference entities here. Nowadays, it became clear to me that, reference planes are very important because they both include reference points and related vectors as well. The definition studied in this post includes a curve […]

This was an interesting topic in design computing class. Geometric constructions based on strict relationships are becoming exciting in parametric modeling environments. I think muqarnas includes such a relationship. There is a primary method of modeling this shape, introduced by Mete Tüneri. His solution to a simple parametric muqarnas object includes a surface with six reference points, with two boolean differences (one cylinder and one box) creating the component. In […]

Here is a funny sketching system for the “SPEC” homework. [GHX: 0.8.0066] Four (or more) points are created using 2d sliders (MD slider) and decomposed these points into x,y and z numbers. Then, they are re-populated in 3d points by changing their plane. X coordinates are connected into Y, and Y coordinates are connected to Z’s. Tricky part comes then, the X number is defined by a serie of numbers started from […]

This is the basic definition of one point attractor on a grid of points. [GHX: 0.8.0066] Here, the fundamentals of data tree matching can be studied. A hexagonal grid is exploded into points and new polygons are created there. Instead of a standard point distance relation to polygon size, this time the distance factor affects the rotational angle of these polygons. Although the structure of data trees is getting complicated, this has no […]

Maybe a huge kitsch for contemporary architecture, I know, but a good example of a fundamental problem of constructing geometric relationships. In ARCH362 today, we’ve examined the geometric modeling process that opens us to parametric relationships just by converting it into a diagram of design history. You may follow the construction of such a diagram step by step and see the possible parameters emerge from it. The only rule of […]

That was about six months ago, our study for a design competition required a spatial allocation algorithm. An office building with a rectangular plot and a strict functional requirement forced me to the good old Voronoi diagrams, subdividing a surface. Here is the definition file: [GHX: 0.8.0066]. However, there were other design parameters such as the sunlight and orientations of each functional cell. Combining a couple of graph components helped me […]

This is the old-method Parametric Truss definition. Interestingly this quickly became a solid solution, used and taught for years. I couldn’t find a better answer yet. As Grasshopper updates, some of the components in this definition change but the overall structure remains. Subdivision of a free-form surface and addition of geometric components has, of course, a wide range of alternatives. Maybe we should combine this with different problems and solutions […]

[GHX:0.8.0066] This is a rather traditional geometry exercise we used to make in MaxScript. Grasshopper is also quite capable of associative geometry and real-time parametric designs of objects. The exercise of designing a furniture family should be based on design research, followed by shape alternatives and sketches (both digital and hand), then might be finalized using this parametric design environment. However, the example presented here is one of the most simplistic […]

In this experiment, I’m trying to use data recorder to change components on a surface. The component part is a standart triangular construction, but the attractor points are defined by a 2D slider that is connected to a data recorder. Data recorder remembers last 15 points, while you move the 2d slider, last 15 points are projected on the base surface. This creates an illusion as if a “snake” game […]

At the initial design phase of an apartment project in İstanbul, Nilüfer Kozikoğlu (TUŞPA Architecture) has offered me a job I haven’t done in Grasshopper before. This definition includes a sketch of a possible apartment renewal, analyzing and optimizing data from the contractor’s and property owners’ perspective. It also checks if the proposed solution is appropriate according to the building regulations for that area. In Turkish, KAKS means the maximum […]

The design of Chinese window lattices named “ice-ray” is one of the classic studies of Shape Grammars. It is an old and good example of algorithmic design. George Stiny explained their geometric construction based on the parametric Shape Grammars approach. He explained shape rules and the abstract machine that produces the subdivisions. I was especially interested in Shape Grammars when I was a graduate student. I even made a prototype […]

In order to start creating recursive algorithms in Grasshopper, I finally managed to run Hoopsnake, a special component developed by Yiannis Chatzikonstantinou. This will help me develop parametric models that include loops. The fundamental experiment here shows a surface subdivision based on iterations. We should define a starting object or data, an operation to be repeated, and a limit that will tell Hoopsnake to stop looping. In this condition, this […]

This is another starting point for pattern generation study in a dataflow environment. I tried to implement the parquet deformation of Islamic patterns in Grasshopper. I studied Hankin’s method of Islamic Pattern generation. Then I tried to simulate his process beginning with basic regular tiling (regular hexagonal tessellation). Craig S. Kaplan (here) explains this and other methods in his dissertation. A Simple Foundation We have already experienced the result of […]

This study includes three main topics related to the basics of Grasshopper. The first one is the surface subdivision, the parametric definition of a surface component, that is, in this case, a simple pyramidal object. The second thing is the associative behavior of surface components with an external parameter, that is another entity in space; a curve. Traditionally, this is simply demonstrated by 1) finding the area centroids of each […]

A previous work showed a method to create interlocking structures to be created without boolean operations. This time, a small addition is made to create waffle objects using two surfaces, one is the top surface, and the other is the bottom. It was a small modification at the beginning; to replace the “extrude” component with an “edge surface” component. But the interlocking details are now different at each intersection, so […]

The regular component design technique can be further improved by adding several manipulations. The purpose of this study was to create a surface component that reacts to an inherent parameter (actually a geodesic curve on the surface). However, within the process of parametric modeling, diverse formal potentials emerged. Most interesting results are achieved by adding a graph parameter to control the waves of reaction while splitting the surface as stripes. […]