Figure 1.
A description of the repeated unit of Orontium aquaticum L. (Araceae) containing five phytomers.
A Schematic image of O. aquaticum [30]. B, Diagram of the repeated unit containing five phytomers [30]. C, A description of B by the covariant of five binary cubics. D, Reducible covariant of five binary cubics corresponded to B. P – prophyll; E – mesophyll; M – monopodial leaf; S – sympodial leaf; X – first phytomer of inflorescence; e – foliage leaf, c – cataphyll, s – sylleptic growth [30]. All morphological terminology and images are from [30].
Figure 2.
Three Fundamental Identitys of CIT and their morphological interpretation (A–C).
The images of phytomers from [31] are re-drawn without buds, reduced phytomers being drawn in a dotted line.
Figure 3.
Basic types of segmentation of a stem, descriptions of Troll's bauplan of angiosperms and the principle of variable proportions.
All images A–E and G–J are re-drawn from [17] and [32] with or without modifications. A, Holocyclic stem [17] constructed from a series of phytomers each occupying the entire diameter of the axis. B, Mericyclic stem [17] constructed from a series of phytomers each occupying only a portion of the whole diameter of the axis. C, The phytomer of mericyclic stem and the corresponded binary quartic. The prophylls, the hypopodium and the mesopodium are not shown. D, The bauplan of the angiosperm plant (“Urpflanze”) [32]. E, Same as D, but built up from the primary root and shoot with mericyclic stem, each phytomer is drawn with the corresponding binary quartic, primary root drawn with the corresponding binary quadratic. F, Brief notation [1] of covariant corresponded to D, E, and H–J. G–J, The principle of variable proportions [32]: the same binary form corresponds to the phytomers themselves or to the parts of the primary thickening and modified shoot axis corresponding to phytomers, that share the same position in bauplan D but generally differ with the shape and/or proportions (G). The phytomers or corresponded parts of a shoot axis are drawn with prophylls/spines [18], [32] and buds/areoles [18], [32]. Each plant H (“Pereskia”, Cactaceace), I (“Cylindropuntia”, Cactaceae), and J (“Ferocactus”, Cactaceae), as well as the bauplan D therefore may be described by a covariant of the kind F.
Figure 4.
Description of the bauplan of monocot seedling and grass embryo by covariants of different binary forms.
A, The image of the bauplan of a monocot seedling from [44], built from primary root, stem, and leaves; (ρx) – linear binary form corresponding to primary root, (ιjx)2 – quadratics, corresponding to hypocotyl (incl. shoot-born roots, coleorhiza and collar) and internodes; (ηjx)2 – quadratics, corresponding to nodes, (φjx) – linear binary forms, corresponding to cotyledon (drawn connected with endosperm) and upper leaves. B, The image of the same bauplan [44], but built from three phytomers (drawn with corresponding binary cubics), all roots are secondary under this view. C–D, The description of a seedling by covariants of ten binary forms (C) of degrees 1–2 or by irreducible covariant of three binary cubics (D). E, Image of a grass seedling from [44]; Co – coleoptile, Ep – epiblast, Mesc – mesocotil, Sc – scutellum, H – hypocotyl (clz – coleorhiza, cr – collar, and r – roots); Lf – leaf. F, Composition of grass seedling if the coleoptile is the first leaf of the plumule, the scutellum being the cotyledon, the reduced phytomer being drawn in a dotted line. G, Composition of grass seedling in the case where scutellum and coleoptile together form a single cotyledon. All morphological terminology from [44].
Table 1.
Descriptions of grass seedling/embryo based on the different treatments of coleoptile.