Lace Experiments
For a research project I participated in in 2024, we generated lace patterns. During this process, I had the opportunity to try out two Grasshopper plugins: Parakeet and Clipper. When combined, they allow you to obtain laser-cutting patterns. Parakeet is a very good plugin that generates tessellations. This was something I always dreamed of developing back in my youth.
2-Uniform Tiling
In this design, I used the Parakeet component named 2-Uniform Tiling. In geometry and tiling theory, a 2-uniform tiling is a type of tessellation where the plane is covered edge-to-edge with regular polygons (equilateral triangles, squares, hexagons, etc.) and contains exactly two distinct types of vertices according to its symmetry group. The configurations used in this particular component are 3.3.3.4.4 and 6.4.3.4. What this means is: we have two types of vertex situations. In the first one, there are three triangles (3) and two squares (4) around a vertex. As you can guess, the sum of the interior angles of these shapes equals 360 degrees (3 x 60 + 2 x 90). The other vertex configuration consists of a hexagon, a square, a triangle, and a square, respectively. The sum of the interior angles of these four shapes is also 360. In short, a nice pattern consisting of triangles, squares, and hexagons is obtained.
Star Pattern II
As the design continued, I connected the 2-uniform tiling to the Star Pattern II component. This component generates a star pattern on the given base using Hankin and Kaplan‘s famous Islamic Pattern method. I don’t fully understand its inputs myself, but what happens here is simply this: the component places an octagon at the midpoints of the cells within the given base and draws lines from its vertices to the midpoints of the cell edges. Since we always use midpoints, continuity is maintained throughout the pattern. By playing with the inputs, you can achieve very different results.
From this point on, I trimmed the pattern with a circular hoop and made it suitable for laser cutting or CNC machining by using the advanced offset capability of the Clipper plugin. As you know, I don’t much like using plugins, and I actually wish I could build these geometric constructions myself. This is why I couldn’t fully understand the inputs for the Star Pattern II component. This time, it felt a bit like taking the easy way out. You can examine the code below. Both plugins need to be installed for the code to run.
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