I had previously shared a few pattern animations (here, here, and here) from 2023 that felt a bit unsettling. Here, I am presenting the last four remaining in the archive of Grasshopper 1.0. To me, they feel a bit eerie, and I don’t even know why I made them this way. But I am sharing them anyway, thinking that maybe they could be useful to someone for a completely different, cheerful purpose. It is possible, but difficult, to create these…

Since I still haven’t been able to upgrade to Windows 11, I am continuing with Rhino 8 and Grasshopper 1. But I think, hopefully, I’ll be able to sort it out soon. In the meantime, I’ll be publishing the last pieces of my remaining archive related to GH 1. Regarding interlocking (waffle) systems, I finally learned how to use the Region Slits component in GH 1, which I had never been able to use until now. I’ve been doing various…

Today’s Digital Culture reading was on Frege. After the historical process shaped by thinkers like Hobbes and Leibniz, and by the effects of capitalism, I thought reading Frege would provide a good foundation before moving on to Wittgenstein. Gottlob Frege (1848-1925) was a German mathematician and logician. He spent most of his academic life at the University of Jena. Regarded as one of the founders of modern logic and analytic philosophy, Frege argued that the foundations of mathematics should be…

Traditionally, when shaping a guitar form, a luthier relies on a combination of craftsmanship and precise geometric tools. This process involves mastering wood-bending techniques around rigid molds, guided by physical templates to achieve the desired acoustic and aesthetic curves. Curves, once more I love talking about this so much. Could my obsession with Bézier curves be OCD? The history of curved shape construction reflects a transformative journey from physical craftsmanship to sophisticated digital computation, primarily driven by the demands of…

The Butterfly Curve is a special planar curve consisting of elegant functions, first described in 1989 by the American mathematician Temple H. Fay in Mathematics Magazine. Its polar-coordinate form is commonly used, though it can also be defined by two parametric functions in Cartesian coordinates. In Praise of Useless Things The Butterfly Curve has no functional role or practical application in modern technology or theory (it is frequently confused with the Lorenz Attractor, to which it is totally unrelated). It…

Leibniz was the topic of last week’s Readings on Digital Culture class. Although he is often presented as one of the ancestors of modern computing and digital technology, I doubt that is entirely accurate. He made big contributions to metaphysics, logic, law, and mathematics. He was also a social butterfly of his age, connected with a large number of people and writing tens of thousands of letters. From an early age, he seems to have an almost infinite desire for…

Revisiting a specific mathematical phenomenon that I previously explored twice, here (in 2017) and here (in 2011), from a different angle in 2026 now. This was the final video (from 2023) that I found in my junk folder during the blog’s resurrection. Today, designers mostly know Fermat through the famous 137.5-degree angle of rotation, which is the mathematical formula used to describe the arrangement of sunflower seeds. However, today I will speculate on a nightmare of Fermat’s. Because Fermat, in…

​The more I work with and study polyhedra, the more I realize how rare and special they are. They represent both the abstract and universal rules of geometry and space. ​I can understand their symmetries, faces, vertices, and most importantly, their mathematical necessities. Yet, when looking at a solid, sometimes a specific form strikes me as more attractive than the others. Moreover, I cannot explain this simply by saying, “It has more symmetry” or “Its proportions are better.” For me,…

I want to introduce a concept I came across the other day, one I had never heard of before, along with a few fantastic websites. The Campanus Sphere is essentially a rather crude spherical representation, the kind I’m used to seeing in (very old) computer games, and it also makes a nice nod to 80s disco culture. I also recall that in many older CAD software packages, spheres and sphere-related Mesh objects were represented as polyhedra using this method. However,…

While digging through my trash archives, I found this video from three years ago. Instead of exploring things with Grasshopper, I jumped into a bit of naive digital art. The Fibonacci Sphere algorithm was very popular in those days. I used the SubD components, which were new at the time. It was around the same period as the one right over there. I tried to make something scary again, but to be honest, there is also quite a depressive mood…