Phyllotaxis

Source: Wikipedia, the free encyclopedia.
Crisscrossing spirals of Aloe polyphylla

In

Ancient Greek φύλλον (phúllon) 'leaf', and τάξις (táxis) 'arrangement')[1] or phyllotaxy is the arrangement of leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature
.

Leaf arrangement

Opposite leaf
Whorled leaf pattern
Two different examples of the alternate (spiral) leaf pattern

The basic

node
) on a stem.

Veronicastrum virginicum has whorls of leaves separated by long internodes.

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 leaf arrangement in Clivia

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 bulbous plants 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.

A Lithops species, showing its decussate growth in which a single pair of leaves is replaced at a time, leaving just one live active pair of leaves as the old pair withers

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[2] 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.[3]

If the arrangement is both distichous and decussate, it is called secondarily distichous.

A decussate leaf pattern
Decussate phyllotaxis of Crassula rupestris

The whorled arrangement is fairly unusual on plants except for those with particularly short

Brabejum stellatifolium[4] and the related genus Macadamia.[5]

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.

Repeating spiral

The rotational angle from leaf to leaf in a repeating spiral can be represented by a fraction of a full rotation around the stem.

Alternate distichous leaves will have an angle of 1/2 of a full rotation. In

Fibonacci numbers
. In some cases, the numbers appear to be multiples of Fibonacci numbers because the spirals consist of whorls.

Determination

The pattern of leaves on a plant is ultimately controlled by the accumulation of the plant hormone

disputed – discuss] When a leaf is initiated and begins development, auxin begins to flow towards it, thus depleting auxin from area on the meristem close to where the leaf was initiated. This gives rise to a self-propagating system that is ultimately controlled by the ebb and flow of auxin in different regions of the meristematic topography.[9][10]

History

See also: Patterns in nature § History

Some early scientists—notably Leonardo da Vinci—made observations of the spiral arrangements of plants.[11] In 1754, Charles Bonnet observed that the spiral phyllotaxis of plants were frequently expressed in both clockwise and counter-clockwise golden ratio series.[12] Mathematical observations of phyllotaxis followed with Karl Friedrich Schimper and his friend Alexander Braun's 1830 and 1830 work, respectively; Auguste Bravais and his brother Louis connected phyllotaxis ratios to the Fibonacci sequence in 1837.[12]

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[13] 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 gradients among the primordia or purely mechanical forces. Lucas numbers rather than Fibonacci numbers have been observed in a few plants[citation needed] and occasionally, the leaf positioning appears to be random.[citation needed]

Mathematics

End-on view of a plant stem showing consecutive leaves separated by the golden angle

Physical models of phyllotaxis date back to

maxons
in the spectrum of linear excitations.

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.[19][20]

In art and architecture

Phyllotaxis has been used as an inspiration for a number of sculptures and architectural designs. Akio Hizume has built and exhibited several bamboo towers based on the Fibonacci sequence which exhibit phyllotaxis.[21] Saleh Masoumi has proposed a design for an apartment building in which the apartment balconies project in a spiral arrangement around a central axis and none shade the balcony of the apartment directly beneath.[22]

See also

Wikimedia Commons has media related to phyllotaxis.

References

  1. Perseus Project
  2. ISBN 978-3-642-55874-0
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  3. ISBN 978-3-642-56306-5
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  4. ^ Marloth R (1932). The Flora of South Africa. Cape Town & London: Darter Bros., Wheldon & Wesley.
  5. ^ Chittenden FJ (1951). Dictionary of Gardening. Oxford: Royal Horticultural Society.
  6. ^ Coxeter HS (1961). Introduction to geometry. Wiley. p. 169.
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  8. PMID 12079669
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  9. S2CID 13800404
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  10. PMID 19090623
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  11. ^ Leonardo da Vinci (1971). Taylor, Pamela (ed.). The Notebooks of Leonardo da Vinci. New American Library. p. 121.
  12. ^
    ISBN 978-0-7679-0816-0
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  14. ^ "History". Smith College. Archived from the original on 27 September 2013. Retrieved 24 September 2013.
  15. PMID 10045303
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  16. S2CID 250864634
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    Levitov LS (January 1991). "Phyllotaxis of flux lattices in layered superconductors". Physical Review Letters. 66 (2): 224–227.
    PMID 10043542
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  18. S2CID 27552596
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  19. ISBN 978-0-486-23542-4
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  20. ^ Adler I. Solving the Riddle of Phyllotaxis: Why the Fibonacci Numbers and the Golden Ratio Occur On Plants.
  21. ^ Akio Hizume. "Star Cage". Retrieved 18 November 2012.
  22. ^ "Open to the elements". World Architecture News.com. 11 Dec 2012.
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