Topiary models (Section 11) present examples of plants subject to the influences of the environment. In nature, interactions between a plant and its environment have often a more complicated character, with the environment affecting the plant and the plant reciprocally affecting the environment. This bi-directional information flow can be conceptualized as the feedback loop shown in Plate 32 (see caption).
Simulation of plants interacting with their environment can be carried out within the general framework of open L-systems [Mec1996]. The development is assumed to take place in a space characterized by a scalar or vector field. Modules of a growing plant can test values of this field at points of interest, and send values that affect the field at specific locations. Sample models constructed according to this scheme are shown below.
Animation 26 (see caption) shows an L-system recreation of one of the earliest models of plant-like branching structures, proposed in 1967 by Cohen [Coh1967]. The model is sensitive to the local density of the growing structure. The gradient of the density function is used to select the least crowded areas available for the further development of each branch. In very dense areas, the growth stops altogether. In this way, the resulting geometry is determined by interactions between the branches, mediated by the environment.
Animation 27 (see caption) shows the development two planar branch tiers competing for space. The underlying model, based on the observation of the tropical tree Terminalia catappa, was proposed by Honda, Tomlinson, and Fisher [Hon1981]. The circles represent leaf clusters, located at the nodes. The endpoint of each branch, or apex, produces new branches, unless they would fall into an existing cluster. This interaction limits the extent of branching, and adapts the shape of each tier to the presence of its neighbor.
Animation 28 (see caption) shows the top view of a ground area with different intensities of incoming light. A hypothetical clonal plant inspired by clover propagates by means of horizontal stem segments (spacers) which connect individual plants (ramets). Old spacers and ramets die. The clone takes advantage of high light intensity by increasing the frequency of branching and decreasing the length of the spacers. Collisions are avoided as in the previous simulation. After colonizing the most favorable bottom left patch, the plant reinvades the top right patch. Light conditions in that patch are not sufficient to continuously sustain the plant. The colony disappears until the patch is reached again by a new wave of propagation. The dynamics of propagation reflects the plant's adaptation to its environment.
Animation 29 (see caption) shows a two-dimensional model of a root seeking water in the soil during its development. The initial water distribution has been predetermined, forming an S-shaped zone of high concentration indicated by the light colour. The growing tips of the main root and rootlets absorb water that diffuses in the soil. The decreased water concentration is indicated by dark areas that emerge around the root system. In areas with insufficient water concentration the rootlets cease to grow before they have reached their potential full length.
Animation 30 (see caption) shows a three-dimensional extension of the previous model, based on the work of Clausnitzer and Hopmans [Cla1994]. Water concentration is visualized by a semi-transparent iso-surface surrounding the roots. As a result of competition for water, the main roots grow away from each other. If the rootlets grow more slowly, the area of influence of each root system is smaller, and the main roots grow closer to each other. This effect is illustrated in Plate 33 (see caption)
Plate 34 (see caption) and Plate 35 (see caption) show a model of a horse chestnut tree inspired by the work of Chiba [Chi1994] and Takenaka [Tak1994]. Here branches compete for light from the sky hemisphere. Clusters of leaves cast shadows on branches further down. An apex in shade does not produce new branches. An existing branch whose leaves do not receive enough light dies and is shed from the tree. In such a manner, the competition for light controls the density of branches in the tree crowns.
In Animation 31 (see caption), two genetically identical trees compete for light. Moving the trees apart after they have grown reveals the adaptation of each crown to the presence of the neighbor tree. A similar adaptation takes place in coniferous tree (Plate 36, see caption, and Plate 37, see caption).
Plate 38 (see caption) further illustrates the impact of competition for light on tree growth. Trees on the border of a stand have assymetrically developed crowns, and retain some of their lower branches. The tree in the middle has lost its lower branches, which did not receive enough light. In the lumber industry, the loss of lower branches is usually a desirable phenomenon, as it reduces knots in the wood and the amount of cleaning that trees require before transport. Simulations may assist in choosing an optimal distance for planting trees, where self-pruning is maximized, yet there is sufficient space between trees to allow for unimpeded growth of trunks in height and diameter.
