#fermat

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…

As studied earlier in Grasshopper here, the sunflower spiral, or Phyllotaxis, or Fermat‘s spiral, could be drawn as an exercise in looping in Rhino Python. Phyllotaxis is the arrangement or patterning of leaves, flowers, or other plant parts around a stem or axis. Thus, it refers to the specific geometric arrangement of these structures in plants. The term “phyllotaxis” comes from the Greek words “phyllon” (meaning “leaf”) and “taxis” (meaning “arrangement” or “order”). Phyllotaxis can vary widely among plant species…

Sunflower Spiral (or Phyllotaxis) can be constructed in Grasshopper according to Vogel’s model of parametric relationships. This model uses polar coordinates. The Grasshopper file is still working after more than 11 years -15.12.2022. This is such a powerful quality of Grasshopper, I think. It’s a good example of utilizing polar coordinates. It’s also fun to play with the parameters and constraints of the Sunflower Spiral. Also, there are very interesting results if you also connect the polar angle value to…