Glossary of Common Terms

• Alternate - see distichous.
• Decussate - 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.
• Distichous - pattern in which a single primordia is inserted at a time and the next primordium is inserted 180° from it. Classified as (1,1).
• Divergence angle (d) - angle between two consecutive primordia.
• Fasciation - 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 F_n+1= F_n + F_n-1 , with initial condition F₀= F₁=1.
• Fibonacci-like sequences - 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).
• Genetic or generative spiral - continuous spiral through consecutively formed primordia.
• 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 137.51^o— is 360^o(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 lattice.
• Hofmeister's rules - primordia initiate periodically at the edge of a circular meristem, at the least crowded spot. They are then radially displaced from the center.
• Meristem (or shoot apex meristem) - growing tip of a plant, usually dome shaped, around which primordia are initiated.
• Multijugate - 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 (k=3).
• Multimerous - whorled. Hence dimerous is 2-wholed, trimerous is 3-whorled etc.
• Node - 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.
• Opposite - decussate.
• 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), ...
• Parastichy - 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.
• Parastichy 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, ....
• Phyllotaxis or phyllotaxy - (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.
• Plastochrone ratio (R) - ratio of the distance of two consecutive primordia from the center of the apex
• Primordia - Microscopic bulges of cells initiating around the apex meristem. Primordia evolve into the different botanical elements of a plant (leaves, petals etc.).
• Rising phyllotaxis - spiral phyllotaxis with increasing parastichy numbers.
• Spiral 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 lattice.
• Whorled (phyllotaxis) 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.
• Whorl - a group of primordia, leaves or other botanical elements, that initiated at almost the same time, at the same node.