Section 12

Table of Contents

Section 14


13. Spiral phyllotaxis

Exogenous control mechanisms may occur not only between a plant and its environment, but also between components of the same plant. We will illustrate this phenomenon using a model of spiral phyllotaxis, or spiral arrangement of organs such as leaves, florets, or seeds. An example of spiral phyllotaxis is shown in Plate 36.

Many models were proposed to explain the emergence of phyllotactic patterns in nature. One of them is the collision-based model, introduced as a biological theory by Battjes [Bat1992], and subsequently applied to image synthesis by Fowler et al. [Fow1992]. The model describes distribution of flower initials, or primordia, on a supporting surface, the receptacle, which determines the shape of the entire structure.

Animation 31 illustrates the operation of this model. The first primordia (shown as yellow half-spheres) differentiate at the base of the receptacle (white). The angle between two consecutively placed primordia, seen from the axis of the receptacle, is equal to 137.5 degrees. The collision-based model assumes this angle as given, but numerous other theories propose explanations of its value. After a certain number of primordia have been placed, a new primordium collides with an existing one. The new primordium is then displaced towards the apex of the receptacle, so that the predefined minimum distance to the closest neighbor is reached. The subsequent primordia are placed at the same level until another collision occurs. Eventually, the entire surface of the receptacle is covered by primordia.

The green coneflower (Rudbeckia laciniata) shown in Plate 37 and the cacti shown in Plate 38 present sample structures generated using this model. In both cases, the primordia have been replaced by models of mature organs.