Geometric substitution using random L-systems

Abstract

Most scientific disciplines rely on models to describe their objects of interest and their behavior. This is also the case in computer graphics where different models are used to describe different entities commonly used in computer graphics systems. Specifically, fractal and procedural models have experienced a recent comeback due to their suitability to represent natural phenomena. Our work mainly concentrates on this area, where we analyze the relationship between geometric substitution techniques and rewrite or symbol pushing systems. Our conclusion is that any substitution rule can be equivalently expressed as a production rule in what we call a random L-system. Random L-systems, however, are more powerful and versatile than earlier techniques like parametric and stochastic L-systems and geometric substitution models. We show in this paper how random L-systems can be used to improve modeling in computer graphics applications. First, we present the model and explain its main features. Then we describe how symbol strings obtained by substitution can be applied to generate both two-dimensional and three-dimensional textures. We also detail how to use local and global perturbations of geometric substitution to obtain realistic models of certain types of objects. Finally, we discuss how the model allows the possibility of generating different level-of-detail geometries of an object, depending on its distance to the viewer. Our main contribution is a new rule-based model, the random L-system, that provides a compact representation for complex procedural objects with added functionality not present in previous models.