Attractive or repulsive interactions in different structure types

Stochastic approaches in phyllotaxis

Theoretical models of phyllotaxis are based on geometric regularities appearing at the level of the shoot apical meristem (SAM). However, one cannot forget the presence of perturbed patterns in many plants. Disorganized patterns found in mutants of Arabidopsis and Antirrhinum bring new theoretical problems that cannot be solved by using models developed to analyse regular phyllotactic patterns. One way to take into account the perturbed patterns is to use a probabilistic approach to phyllotaxis. This review will focus mainly on recent probabilistic approaches that can be used to analyse perturbed patterns found in the plant kingdom in general and in phyllotactic mutants in particular. More precisely, it will be shown how probabilistic approaches can be used to determine the degree of order of phyllotactic patterns. By using particular tests, it is possible to statistically differentiate between whorled and distichous patterns (aggregated dispersion), spiral patterns (uniform dispersion), and random patterns (random dispersion). The elaboration of a general probabilistic model of phyllotaxis represents a new challenge for both theoretical and experimental research.

Characteristic Lattice Complexes

2D and 3D lattice complexes with increased self-coordination numbers Ti , i = 1–3, of nearest, second and third neighbors were derived for characteristic Wyckoff sets with zero or one parameters. Structure types of adsorbed atoms in 2D or elements A in 3D and A x B y compounds are approximated to the list of lattice complexes. Covalent bonding or electronic effects of atoms like lone electron pairs or Jahn–Teller distortion give rise to deviations from lattice complexes. Homogeneous structures A x B y with identical A–A or B–B self-coordination numbers T 1, T 2, T 3 of nearest, next-nearest and third neighbors are selected for different systems like magnetic ordering with A = ⊕ and B = ⊖ spin direction or crystals of organic molecules with different orientations.