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In botany, phyllotaxis (), or phyllotaxy is the arrangement of leaf on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature.
With an opposite leaf arrangement, two leaves arise from the stem at the same level (at the same node), on opposite sides of the stem. An opposite leaf pair can be thought of as a whorl of two leaves.
With an alternate (spiral) pattern, each leaf arises at a different point (node) on the stem.
Distichous phyllotaxis, also called "two-ranked leaf arrangement" is a special case of either opposite or alternate leaf arrangement where the leaves on a stem are arranged in two vertical columns on opposite sides of the stem. Examples include various bulb such as Boophone. It also occurs in other plant habits such as those of Gasteria or Aloe seedlings, and also in mature plants of related species such as Kumara plicatilis.
In an opposite pattern, if successive leaf pairs are 90 degrees apart, this habit is called decussate. It is common in members of the family Crassulaceae Decussate phyllotaxis also occurs in the Aizoaceae. In genera of the Aizoaceae, such as Lithops and Conophytum, many species have just two fully developed leaves at a time, the older pair folding back and dying off to make room for the decussately oriented new pair as the plant grows.Heidrun E.K. Hartmann (2012). 9783642563065, Springer Science & Business Media. . ISBN 9783642563065
If the arrangement is both distichous and decussate, it is called secondarily distichous.
The whorled arrangement is fairly unusual on plants except for those with particularly short internodes. Examples of trees with whorled phyllotaxis are Brabejum stellatifolium and the related genus Macadamia.
A whorl can occur as a basal structure where all the leaves are attached at the base of the shoot and the internodes are small or nonexistent. A basal whorl with a large number of leaves spread out in a circle is called a rosette.
Alternate distichous leaves will have an angle of 1/2 of a full rotation. In beech and hazel the angle is 1/3, in oak and apricot it is 2/5, in sunflowers, Populus, and pear, it is 3/8, and in willow and almond the angle is 5/13. The numerator and denominator normally consist of a Fibonacci number and its second successor. The number of leaves is sometimes called rank, in the case of simple Fibonacci ratios, because the leaves line up in vertical rows. With larger Fibonacci pairs, the pattern becomes complex and non-repeating. This tends to occur with a basal configuration. Examples can be found in Asteraceae and seed heads. The most famous example is the sunflower head. This phyllotactic pattern creates an optical effect of criss-crossing spirals. In the botanical literature, these designs are described by the number of counter-clockwise spirals and the number of clockwise spirals. These also turn out to be Fibonacci numbers. In some cases, the numbers appear to be multiples of Fibonacci numbers because the spirals consist of whorls.
Insight into the mechanism had to wait until Wilhelm Hofmeister proposed a model in 1868. A primordium, the nascent leaf, forms at the least crowded part of the shoot meristem. The golden angle between successive leaves is the blind result of this jostling. Since three golden arcs add up to slightly more than enough to wrap a circle, this guarantees that no two leaves ever follow the same radial line from center to edge. The generative spiral is a consequence of the same process that produces the clockwise and counter-clockwise spirals that emerge in densely packed plant structures, such as Protea flower disks or pinecone scales.
In modern times, researchers such as Mary Snow and George Snow continued these lines of inquiry. Computer modeling and morphological studies have confirmed and refined Hoffmeister's ideas. Questions remain about the details. Botanists are divided on whether the control of leaf migration depends on chemical among the Primordium or purely mechanical forces. rather than Fibonacci numbers have been observed in a few plants and occasionally, the leaf positioning appears to be random.
Close packing of spheres generates a dodecahedral tessellation with pentaprismic faces. Pentaprismic symmetry is related to the Fibonacci series and the golden section of classical geometry.
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