Abstract

Plant morphogenesis exhibits numerous bifurcations with particular angle values such as 41°, 53°, which, in lower plants, can be measured in the thallus, and, in higher plants, in the ribs of the leaves. An interpretation of these angles is attempted. Since they characterize the functioning of a morphogenetic field, a formalism was constructed suitable for the study of living systems. The mathematical tool devised here, named the Arithmetical Relator, combines Geometry and Arithmetic, and assumes that a general system results from the interaction between an internal cyclic structure and an environment to which this structure is adapted. The formalism described therefore takes into account partial self-reference and changes in the level of organization. Within this framework, the particular values of the ramification angles are extreme for slight shifts in the internal structure. A pattern of the relations between the genome, the cell and the organ is suggested.