Algorithms

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…

While looking at the student works of my 2009 class, I realized that in some cases, the “pipe” component takes a considerable amount of time to execute even on fast computers. Students mostly create pipes to model structural frame systems such as canopies and facade frames. Therefore, the path of the pipe is usually linear (not curved). I decided to calculate the performances of three approaches that could be used to make pipes in Grasshopper. One was the good old…

Force fields might be one of the most influential component sets of Grasshopper. Thus it also becomes a de-facto standard design approach like the Voronoi subdivision. There are beautiful examples of this mathematical solution. Here is a good explanation of mathematics underneath, and here are my previous studies. I tried to use the Grasshopper’s force field components and see how it looks like when animated. Thus, multiple spin forces are merged together in this definition. Therefore, the overall effect of field…

While searching for a way to work with random points and growing populations, this idea appeared accidentally. I wasn’t trying to mimic the behavior of Karyokinesis of biological cells (in fact I’m in serious doubt about biomimicry in general). The trick is to use a timer + data recorder + a knob for the arbitrary user input. It starts to breed when you start the timer, but to change the evolution speed, just roll the knob!  Of course, the knob…

This was the initial example of image processing in our Parametric Modeling class. Hand-drawn and digital diagrams can also be digitized and used in order to describe certain parameters for design formation. Such algorithms would similarly use the Image Sampler Component of Grasshopper. In the algorithm below, image data is used to capture black pixels as attractors of a Voronoi subdivision. A regular point grid is dispatched according to Brightness values so that the points that lie on the lines of…

Grasshopper still surprises me. This definition draws a spiral by using a random component. It is obvious that the seed value of the random component has a relationship with an archimedean or a similar spiral. My intention was to create a definition to put a number of random points inside a circular area, not a rectangular one. While I grow the radius of a circle and get a t parameter evaluation from a random component using the same seed value…

I at the Center is a multiple-axes vertex deformation based on a quadrangular hyperframe, designed by David Oleson at the studio of William Huff in 1964. Below, you see the original drawing and my Grasshopper animation based on a single-point attractor, creating the “I” wherever it is. It was a pleasure to read and repeat this deformation, which is a nice exercise in data tree operations and also one of the first examples I see about point attractor algorithms in design…

This simple vb.net component controls the Rhino viewport background without a need to enter its options panel. It is used to change the viewport background color and grid visibility quickly within Grasshopper. Here is the definition file: [GHX: 0.9.0056]. In order to be able to return to default settings, I put a “default” toggle. Just click on it to “false” state, then the Rhino background color can be changed by the B input. This component also handles the grid. However I…

Instead of searching for an iterated and rule-based variety, this method captures instances of spatial deformation by transforming the hyperframe. This liberates us from a classical understanding of pattern deformations that are enframed within regular polygons, mostly rectangles or hexagons. Grasshopper has a built-in component to study such variety. The spatial Deform component gets vectors as inputs and transforms any given geometric object according to it. This website has also another nice use of this component.

Fracture is a simple effect experiment on Grasshopper. Although it is not the best tool for an interactive media installation regarding its performance, I tried to use it as a simple sketching tool for concept development. It is the sketch of a material system we are working on nowadays for an Exhibition. The initial diagram of Grasshopper includes a nested Voronoi subdivision broken by moving attractor points. It is not fast enough for a real-time interaction yet, because of the…