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 32 (see caption) 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 40 (see caption) and the cacti shown in Plate 41 (see caption) present sample structures generated using this model. In both cases, the primordia have been replaced by models of mature organs.
