Generation of 3-dimensional plant bodies by double wall map and stereomap systems

Abstract

The seven described archetypes of development (Table 1) cover all developmental possibilities for systems with parity and a unique cell boundary length of 4, 5, or 6 (column (a)). The geometrical constraints given by the quantification of wall lengths according to the number of segments of which they are composed, lead in some cases to 3-dimensional plant bodies described by the cellular arrangement in their epidermis. All archetypes exhibit very common botanical features. Real organisms differ essentially from archetypical ones by non uniform lifespans of cells and finite mitotic activity of most cells. The relationship between maps respecting various lifespans and the corresponding archetype will be the object of a separate publication.

Stereomaps, representing double wall regions in 3-dimensional space, are somewhat difficult to interpret geometrically. In the case of systems with parity, the upcoming constraints, given by the edge length specification, will very often lead to impossibilities, as not any more dimension is available. In this case, cells become either smaller or stop to divide. This is a typical case of division stop under geometrical constraint (cf. A. Paz, this volume).