| |
Introduction to Phyllotaxis [Greek
phyllo, leaf + taxis, arrangement]
This page presents some of the themes explored in this site.
Each theme is linked to a page which opens to an exploration of
that theme. For a more leisurely introduction, you can go to the
site for our exhibit at the Smith Botanic Garden.
|
|
|
| |
Most arrangements of leaves fall into 3 or 4 main categories:
spiral, distichous, whorled, and multijugate. Spiral arrangements
are most frequent and they are classified by the number of spirals
(parastichies) they exhibit. Mathematically, all these patterns
are types of lattices.
|
 |
|
| |
The number of visible spirals (parastichies) in spiral arrangements
are most often Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21 ...)
and the angle between successive leaves is close to the Golden
Angle - about 137.5 degrees. This frequent type of pattern is
called Fibonacci phyllotaxis. Fibonacci numbers and the Golden
Angle have a precise mathematical relationship.
|
 |
|
| |
Microscopic Formation of Plant Patterns
Leaves and other botanical elements initiate as microscopic bulges
of cells at the growing tip of a plant, forming lattice-like patterns.
|
|
|
| |
Mathematical Model
A simple mathematical model based on the botanist Hofmeister's
observations can account for Fibonacci phyllotaxis.
|
 |
|
| |
So ... Do Plants Know Math?
Phyllotaxis has affinities to other pattern formation mechanisms
where many simple agents interact with simple rules. What are
the evolutionary advantages of Fibonacci phyllotaxis?
|
 |
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
| |
|
|
|
