SIMULATING TREES USING FRACTALS AND L-SYSTEMS

摘要

Algorithmic simulation of natural environments in a convincing manner presents an ongoing challenge to modelers and developers. Of particular challenge in simulating natural environments is the dynamic creation of botanical forms, that is, plants. Many plants exhibit complex structural forms that defy traditional geometric patterns, and as such, are difficult to simulate in a convincing way using traditional geometric and mathematical constructs. Using statically modeled techniques is cumbersome, especially when faced with the challenge of producing multiple similar, yet unique plant forms, such as found in a forest of trees. To adequately recreate a convincing organic environment, some dynamic and stochastic model is necessary. While the shape and structures of plants, particularly trees, often appear irregular and chaotic, they also exhibit a high degree of self-similarity. Self-similarity suggests a recursive or iterated approach to the dynamic modeling of botanical forms. As such, constructs such as fractal geometry and Lindenmayer systems seem prime candidates for the generation of such forms. This paper explores the use of fractal geometry as the basis of simulating the forms of trees. Lindenmayer systems (L-Systems), iterated function systems (IFS), their relationships, and their use in simulating trees are discussed. The primary focus of this paper is to present and explain the tree simulation software written for our implementation by extending the Honda model to include stochastic simulation.