of Common Terms
- whorled pattern with two primordia
in each whorl - classified as 2(1, 1) or (2,2).
- Discrete dynamical system
- a function on a set, which is iterated. The
dynamical system(s) in this web site act on divergence angles
of configurations and their stationary solutions are spiral lattices.
The main branch of stationary solutions has Fibonacci phyllotaxis.
- pattern in which a single primordia
is inserted at a time and the next primordium is inserted 180°
from it. Classified as (1,1).
angle (d) - angle
between two consecutive primordia.
- elongation of the meristem resulting in irregular phyllotaxis.
- Fibonacci sequence
- 1, 1, 2, 3, 5, 8, 13 . . . each is
the sum of the previous two. Defined by the recurrence relation
Fn+1= Fn + Fn-1 , with initial
condition F0= F1=1.
- have the same recurrence relation as the Fibonacci sequence,
but may start with different F0, F1. The
most common in plants after the Fibonacci sequence is the Lukas
sequence, with F0= 1, F1= 4.
- Fibonacci phyllotaxis
- spiral arrangements (or lattices) in which the number of parastichies
are consecutive Fibonacci numbers.
- Fundamental theorem
of phyllotaxis - In spiral phyllotaxis, this theorem
(proven in different versions by Bravais, Adler, Jean, Hotton)
gives the intervals of divergence angles within which it is possible
to see a given phyllotaxis type (m,n).
or generative spiral
- continuous spiral through consecutively
- Golden mean
or golden ratio F = (1+sqrt(5))/2
~ 1.61803 is the limit of quotients of successive Fibonacci numbers.
Presumed to occur in Greek and Renaissance art and architecture.
- Golden angle
- angle that appears between botanical elements of plants showing
Fibonacci phyllotaxis. This angle —about 137.51o—
is 360o(2-F) where F
is the golden mean.
- Helical lattice
- arrangement of points on regularly spaced circles around a cylinder,
with one point per circle and with constant (divergence) angle
between successive points. Model for helical phyllotaxis.
- Helical phyllotaxis
- phyllotactic pattern where the elements are arranged as a helical
- Hofmeister's rules
- primordia initiate periodically at the edge of a circular meristem,
at the least crowded spot. They are then radially displaced from
(or shoot apex meristem)
- growing tip of a plant, usually dome shaped, around which primordia
- also called spiro-whorled - phyllotactic
pattern with several primordia at each node. The parastichy numbers
(n,m) have a common divisor in multijugate phyllotaxis: (n,m)=(ki,kj)
(also denoted (k(i,j)), where k is the number of primordia at
each node. With this notation, the term k-jugate
is also used, as are bijugate
(when k=2) and trijugate
- whorled. Hence dimerous
is 2-wholed, trimerous is
- where a leaf or primordium attaches to the stem.
- Node numbers - the numbers obtained by counting the vertically ordered node, assigning 0 to a specific node.
- Orthostichy - commonly refers to an almost vertical row of leaves along a stem, usually following the main vasculature of the stem. In helical phyllotaxis with parastichy numbers n and m, an orthostichy connects a node q to ..., q-2(n+m),q-(n+m), q, q+(n+m), q+2(n+m), ...
- usually refers to the spirals in
plants visible to the eye, joining each element (primordia, leaf,
scale, floret) to its nearest neighbors. Parastichies usually
come in two families winding in opposite directions.
numbers - The
numbers of parastichies in the two families — denoted by a pair (n,m)— Parastichy numbers classify
spiral and whorl phyllotaxes. In helical phyllotaxis, one of the parastichies through node q connect the nodes ..., q-2n,q-n, q, q+n, q+2n, .... and the other likewise for..., q-2m, q-m, q, q+m, q+2m, ....
- (Gr. Phyllo - leaf + Taxis
- arrangement) The study of the arrangement of repeated units
such as leaves around a stem, scales on a pine cone or on a pineapple,
florets in the head of a daisy, and seeds in a sunflower. Also
refers to specific arrangements (e.g.. (3,5) spiral phyllotaxis).
The main different types of phyllotaxes are spiral, multijugate,
distichous and whorled - the last two can be seen as special cases
of the first two.
ratio (R) - ratio
of the distance of two consecutive primordia from the center of
- Microscopic bulges of cells initiating
around the apex meristem. Primordia evolve into the different
botanical elements of a plant (leaves, petals etc.).
- spiral phyllotaxis
with increasing parastichy numbers.
lattice - arrangement
of points on concentric circles with radius increasing at a constant
rate and with constant (divergence) angle between successive points.
Can be obtained as the set of integer powers of a single complex
number. Model for spiral phyllotaxis.
- Spiral phyllotaxis
- phyllotactic pattern where the elements are arranged as a spiral
several primordia are initiated at essentially the same time and
are spread out equally around the circumference of the meristem.
Moreover the directions of the primordia at a node bisect those
of the previous node. This last fact is sometimes emphasized by
the qualifier alternating whorls
in contrast to spiro-whorled
(multijugate). Classified as (k,k), where k is the number of primordia
per whorl. The terms multimerous and verticillate
are synonimous to whorled phyllotaxis.
- a group of primordia, leaves or other botanical elements, that
initiated at almost the same time, at the same node.