# Phyllotaxis

## Definitions

• Webster's Revised Unabridged Dictionary
• n Phyllotaxis (Bot) The order or arrangement of leaves on the stem; the science of the relative position of leaves.
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Century Dictionary and Cyclopedia
• n phyllotaxis In botany, the distribution or arrangement of leaves on the stem; also, the laws collectively which govern such distribution. Leaves are distributed so as to economize space and give a good exposure to light; and to accomplish this they are arranged in a variety of ways, which all fall under two principal modes. These are the verticillate or cyclical, in which there are two or more leaves at the same height of the stem, and the alternate or spiral, in which the leaves stand singly, one after another. In the verticillate arrangement the leaves form a succession of whorls or circles around the stem, with two, three, four, five, or more in each whorl. In the alternate or spiral arrangement the leaves are distributed singly at different heights of the stem and at equal intervals. The simplest is the two-ranked or distichous arrangement, which prevails in all grasses, in the linden, elm, etc., in which the leaves are disposed alternately on exactly opposite sides of the stem. The second leaf is therefore the furthest possible from the first, and the third is the furthest possible from the second. and consequently is exactly over the first, and so on. They thus form two vertical ranks in which the angular divergence is half the circumference, or 180°. In all cases the angular divergence may be represented by a fraction, in which the numerator designates the number of turns of the spiral that are made in passing from one leaf to the next one that is precisely vertical to it, while the denominator expresses the number of vertical rows thus formed, from which the class of phyllotaxis takes its name, as the tristichous or three-ranked (⅓), the pentastichous or five-ranked (⅖), the octostichous or eight-ranked (⅜), and even as high as a thirteen-ranked () phyllotaxis has been made out.
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Chambers's Twentieth Century Dictionary
• n Phyllotaxis fil-ō-tak′sis the disposition of leaves on the stem
• Phyllotaxis Also Phyll′otaxy
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## Etymology

Webster's Revised Unabridged Dictionary
Phyllo-, + Gr. ta`xis order

## Usage

### In literature:

Phyllotaxis, Darwin and Falconer on.
"More Letters of Charles Darwin Volume II" by Charles Darwin
The subject of leaf-arrangement should be passed over until phyllotaxy is taken up.
"Outlines of Lessons in Botany, Part I; From Seed to Leaf" by Jane H. Newell
Thus, the leaves in assuming a new phyllotaxy, take one quite analogous to the normal one.
"Vegetable Teratology" by Maxwell T. Masters
This is the leaf-arrangement or phyllotaxy of the apple-tree, expressed by the fraction 2/5.
"The Apple-Tree" by L. H. Bailey
Four quadrangular scales in mutual contact represent the condition of definite phyllotaxis.
"The Genus Pinus" by George Russell Shaw
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### In science:

Adler I, Barabe D, Jean RV (1997) A history of the study of phyllotaxis.
Magnetism, FeS colloids, and Origins of Life
Levitov LS (1991) Fibonacci numbers in botany and physics: Phyllotaxis.
Magnetism, FeS colloids, and Origins of Life
Selvam AM (1998) Quasicrystalline pattern formation in ﬂuid substrates and phyllotaxis.
Magnetism, FeS colloids, and Origins of Life
Jean R. V., 1994, Phyllotaxis : A systemic study in plant morphogenesis, Cambridge University Press,.
Randomness and Multi-level Interactions in Biology
One of Turing’s main achievements was to come up with mathematical descriptions — differential equations — governing such phenomena as Fibonacci phyllotaxis: the surprising showing of Fibonacci progressions in such things as the criss-crossing spirals of a sunﬂower head.
Definability in the Real Universe
In his formulation of the Hypothesis of Geometrical Phyllotaxis he expressed simple rules adequate for the appearance of Fibonacci pattern.
Definability in the Real Universe
The basic principle of phyllotaxis has been formulated as early as 1868 by Hofmeister and states that each new structure (leaf, ﬂoret, seed,etc.) appears ”opposite” to the previous one - or ones.
Fibonacci numbers in phyllotaxis : a simple model
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