Classification
There are four main types of phyllotaxis, as shown below. They can be detected and further classified by the number of visible spirals (parastichies) they display. All of these patterns can be modeled by simple lattice-like mathematical structures. Other patterns may exist that are not as regular and therefore seldom mentioned by botanists.
Spiral Phyllotaxis
In spiral phyllotaxis, botanical elements grow one by one, each at a constant divergence angle d from the previous one. This is the most common pattern, and often the divergence angle d is close to the Golden Angle (≈137.5°).
Multijugate Phyllotaxis
In multijugate phyllotaxis, two or more botanical elements (two in the example above) grow at the same node. Elements in a whorl (group of elements at a node) are spread evenly around the stem and each whorl is at a constant divergence angle d from the previous one.
Distichous Phyllotaxis
In distichous phyllotaxis, leaves or other botanical elements grow one by one, each at 180 degrees from the previous one.
Whorled Phyllotaxis
In whorled phyllotaxis, two or more (three in the example above) elements grow at the same node on the stem. Elements in a node are evenly spread around the stem, midway between those in the previous node.
Counting Spirals
To further classify spiral and multijugate patterns, one counts the number of visible spirals, called parastichies, which join each element to its nearest neighbors. These spirals normally come in two families, yielding a pair of numbers called parastichy numbers. If the parastichy numbers have no common divisor other than 1, the pattern is a spiral phyllotaxis. If the parastichy numbers do have a common divisor k, then the pattern is multijugate (more precisely k-jugate) and there are k elements at each node. The notion of parastichy numbers can be extended to distichous phyllotaxis with parastichy numbers (1,1) and whorled with parastichy numbers (k,k).
This Aeonium has parastichy numbers (2, 3). Since 1 is the only common divisor of 2 and 3, this is a spiral pattern. Since spiral phyllotaxis can be viewed as 1-jugate, the notation 1(2,3) is also used for this pattern.
This Gymnocalycium has parastichy numbers
(10, 16). which have the common divisor k=2. Hence this is a multijugate pattern (more precisely 2-jugate). The notation 2(5, 8) is also used to classify this pattern.
The classification of a phyllotactic pattern (of the 4 above varieties) is given by its pair of parastichy numbers (m,n). If k is the greatest common divisor of m and n, and m=ki, n=kj, the notation k(i, j) may be used. The number k represents the number of elements per whorl. When k =1, the configuration is a spiral, when k>1 and i=j, it is whorled or k-merous, and when k>1, and i, j are distinct, it is called multijugate or k–jugate). As special cases, (1, 1) configurations are called distichous, and 2-whorled (or dimerous) patterns, 2(1,1), are called decussate. The configuration is a Fibonacci phyllotaxis when the parastichy numbers are successive elements in the Fibonacci sequence.