​In this article, I will attempt a small intervention in contemporary artificial intelligence discussions with an old philosophical example. Our hypothesis is this: ​”Artificial intelligence is very powerful at defining and reproducing existing patterns. However, experiencing that which is not there, absence, negation, and nothingness, as a lived condition belongs exclusively to human consciousness.” Jean-Paul Sartre, in his famous “Cafe Example” from his 1943 work “Being and Nothingness“, describes the experience of someone entering a crowded cafe to find a…

The logic of computer programming has fascinated me since childhood. The same way of thinking also lies behind design mathematics, which is now my main field of interest. Searching for the simplicity behind things, looking for the fundamentals, and identifying the most meaningful basic elements has always been my greatest challenge. With this intention, Designcoding went online in 2011. I tried to share my research, some student work, and news. While learning computational geometry, I wanted to teach it as…

Exploring dual polyhedra in Grasshopper is an interesting topic. In this post, I try to generate the dual of any polyhedron using Rhino Python and possibly Grasshopper. I developed this code for Rhino Python earlier here, and now I have converted it into a Grasshopper-Python component for better usability. I start the process by breaking the polyhedron into individual faces and gathering the corner points of each face. These points become the vertices of the dual polyhedron. Then, for each…

String art is a cool art technique that combines geometry and aesthetics to recreate images using lines between pins. Here is a good reference to start studying it. In this post, I explored a custom Rhino Python script designed for Rhinoceros 7 and 8. It transforms a grayscale image into a dense web of threads. The algorithm analyzes the darkest areas of the image and connects pins in a circular layout to form compositions. The script begins by converting a…

Differential growth is a process where different parts of a structure grow at different rates, leading to complex forms. After watching this, I decided to try it in Grasshopper. Here, differential growth mimics this behavior by applying rules such as Repulsion to avoid crowding or overlapping, Cohesion to keep parts connected or within a range, and Insertion to add new elements when a part stretches too far. The algorithm I present here simulates a differential growth process starting from a…

An aperiodic tiling is a pattern that covers the plane without ever repeating itself (i.e., it is non-periodic). A few special shapes, arranged according to specific rules, can cover the entire plane, but the resulting pattern never repeats exactly. I challenged myself on a 3-day coding sprint to create a general-purpose script in Grasshopper that could generate these tilings. I set Socolar Tiling as my first target. This link contains great information about this and many other aperiodic tilings. Socolar…

The Fourier Transform is a powerful mathematical technique that allows us to analyze the different frequency components within a signal or shape. Its discrete version, the Discrete Fourier Transform (DFT), is used when working with numerical data. I studied the Fourier Series here before. One of the most fascinating aspects of the DFT is that it can represent a signal or shape using rotating circles (or vectors). Each circle corresponds to a specific frequency, amplitude, and phase. When connected in…

In large-scale projects, calculating tiling layouts for wall, floor, and ceiling surfaces becomes even more critical. Evolutionary optimization of these tilings seemed to be a viable approach yesterday. Considering how time-consuming and labor-intensive this process can be, I tried using Galapagos, an old but often overlooked feature in Grasshopper, which might be particularly useful in this situation. Galapagos provides an alternative interface for evolutionary optimization within Grasshopper. It works by minimizing or maximizing a fitness value you define, using parameters…

Although it appears simple, Goldberg Polyhedra in Grasshopper became a tough challenge, which I like a lot. I spent about 24 hours attempting to generate these polyhedra. I started with Goldberg’s original method. This creates an equilateral triangle using coordinates denoted as m and n on a hexagonal grid. Then, we place this triangle onto the faces of an icosahedron. Finally, we project them onto a concentric sphere. We can create many polyhedra by changing the values of m and…

The Hilbert Curve is one of the results of David Hilbert’s vision of mathematics as a network of symbolic systems. Defined in 1891, this curve is a fractal that fills a two-dimensional plane with a one-dimensional line in the limit. It exhibits self-similarity. It emerged from representing higher-dimensional spaces through continuous, lower-dimensional entities. A curve that grows within a bounded area remains continuous but non-differentiable. Yet it possesses infinite length. Perhaps no one will ever truly see or fully grasp…