Fermat’s Spiral with Rhino Python
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.
import rhinoscriptsyntax as rs
import math
s = 137.508
for n in range(0,500):
t = math.sqrt(n)
g = n * s
z = rs.Polar([0,0,0],g,t)
rs.AddCircle(z,0.3)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 and often follows specific mathematical patterns. One of the most well-known patterns is the Fibonacci sequence, in which each number is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5, 8, 13, …). In some plants, the number of spirals or whorls of leaves or other plant parts follows the Fibonacci sequence. This results in a visually appealing arrangement.
If you are new to Rhino Python, you may wonder how you are going to write this code. Just type EditPythonScript in the Rhino command bar and open the Python editor. Then write the code shown above and press F5 to run it. Alternatively, I prepared a Grasshopper definition including the same Python code as a component. Here it is:
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