Welcome to Phyllotaxis, the field studying these patterns!

This website sketches the various descriptions of phyllotaxis, and biological mechanisms. You will be able to travel in the universe of spiral patterns and play with developmental models. You’ll be invited to an overview of the fascinating history behind phyllotaxis, involving natural phyllosophers, a crystallographer explorer of the pole, a mathematician father of the computer and secret warrior of WWII, a physicist sliding down the dunes of the world.

Fibonacci Phyllotaxis

One central phenomenon in Phyllotaxis is that many plants display numbers of parastichies that are pairs of successive numbers in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 …

The pine cone shown has parastichy numbers 8 and 13, the sunflower has 34 and 55.

When the Fibonacci pattern is nice and regular, the angle between successive elements is close to the Golden Angle
~ 137.51^o = 360^o (2 – phi), where phi is the Golden Mean.

Once Fibonacci phyllotaxis was observed in the early 1800’s, scientists of all persuations attempted to describe it, and explain it physically, mathematically and biologically. Our understanding progressed with the technology: microscope, computer, and modern molecular biology.

Yet, much remains un-explained. How do patterns transition between different Fibonacci numbers as they grow? What can we say of all the plants that do not exhibit Fibonacci phyllotaxis ?The strawberry above has parastichy numbers 14 and 15, an example of “quasi-symmetric” phyllotaxis, for instance.