Plant Spirals:
Virtual Tour 




Out of all nature's patterns, this exhibit concentrates on the spiral patterns ubiquitous in plants. A simple mathematical model captures the essence of the phenomenon. Enter a panel by panel tour of the exhibit here, or click on a picture to enter the tour at that station. You can also see a Quick Time movie of the exhibit. 

Fibonacci Numbers and Golden AngleThe numbers of spirals are most often successive Fibonacci numbers (1, 1, 2, 3, 5, 8 ...). When this is the case, the angle between successive elements is close to the Golden Angle, about 137.5 degree. What is the relation between Fibonacci numbers, Golden Angle and Golden Mean? How did these notions occur in history? 
Spirals Under the MicroscopeSpirals initiate at the microscopic tip of the plant (meristem) as arrangements of bulges of cells (primordia). These patterns propagate throughout the life of the plant.


Hofmeister's Rules and Math ModelA math model (dynamical system) accounts for the phenomenon, given the rules derived from the botanist Hofmeister's observations: primordia initiate periodically around the meristem in the least crowded space. The math model was inspired by the physical model of Douady and Couder.

Universe of Spiral LatticesConfigurations of points with constant divergence angle are called spiral lattices. In the dynamical model, configurations often converge to very specific spiral lattices: those exhibiting Fibonacci numbers of spirals. A partition of the universe of spiral lattices shows how these Fibonacci lattices lead the way to the Golden Angle.

So, Do Plants Know Math?They don't have to ... Plants only need to set the stage for Hofmeister's rules. What are the common features this model shares with other pattern formation mechanisms? What evolutionary advantage do the spiral patterns express?
