Section 10 Table of Contents Section 12

11. Exogenous control of plant development

Diffusion-limited aggregation and cellular automata provide models of exogenous mechanisms of branching pattern formation. In this case, components of the growing structure communicate through the surrounding space. In contrast, L-systems simulate endogenous control mechanisms, which rely on information flow within the developing structure. Both lineage and interaction between adjacent modules are forms of endogenous control.

In nature, endogenous and exogenous control mechanisms are often combined. For example, the development of a tree is affected by the genetically controlled formation of meristems (apices), the flow of water, nutrients, and phytohormones through the branching structure, and the plant response to environmental factors, such as the shading and crowding of branches. Environmentally-sensitive L-systems represent one of the approaches proposed to create comprehensive models integrating endogenous and exogenous phenomena [Pru1994c]. In this case, development is assumed to take place in a space characterized by a scalar or vector field. Modules of a growing plant test values of this field at points of interest.

For example, Animation 23 (see caption) presents the operation of an environmentally-sensitive L-system simulating the response of a simple two-dimensional branching structure to pruning. The developing structure is confined to a square, and the apices test whether they are within or outside this area. During the initial phase of development the apex of the main axis creates a sequence of internodes and dormant buds. After crossing the bounding square the apex is pruned and a signal activating the nearest dormant bud is sent basipetally. The activated bud initiates a lateral branch, which grows in the same manner as the initial structure (traumatic reiteration). After crossing the bounding square, the apex of the reiterated branch is also pruned, and the bud-activating signal is generated again. The final structure results from the repetition of this process.

Three-dimensional extensions of the above model are shown in Animation 24 (without leaves, see caption), and in Animation 25 (with leaves, see caption). In both cases, some of the newly created buds initiate new branches spontaneously, yielding tree-like structures. Pruning constrains the outline of the growing plants to a cubical bounding box, and increases the density of branches and leaves near the box boundaries.

The pruning of plants to elaborate ornamental shapes is termed topiary. For example, Plate 26 (see caption) and Plate 27 (see caption) shows a plant confined to a bounding volume defined as the union of parallelepiped and a cylinder. Plate 28 (see caption) shows a pair of trees pruned to a spiral shape. Plate 29 (see caption) incorporates these and other trees pruned to a variety of shapes into a synthetic image of a topiary garden, inpired by the Levens Hall garden in England [Coa1963]. Plate 30 (see caption) presents a more complex bounding volume resembling a dinosaur. It has been constructed as an implicit surface defined by the skeleton of lines and ellipsoids. Plate 31 (see caption) shows the result of pruning a pair of trees to this dinosaur shape.

Section 10 Table of Contents Section 12