L-system fractals (Q879243)

The book provides a comprehensive survey of important aspects of fractals to be generated by iterated function systems and Lindenmayer systems (L-systems). It begins with an introduction to fractals, computer graphics and L-systems. The next chapter contains a detailed survey of fractals and L-system concepts including a historical overview and a review of literature. Two principal applications of L-systems, namely the generation of fractals and the realistic modeling of plants, are discussed, too. The third chapter is devoted to the interactive generation of fractal figures using iterated function systems based on iterated geometric transformations (translation, dilation, rotation reflection, inversion). The formulation of mathematical equation for generating fractal figures is emphasized and the iterated functions for self-similar images are discussed. It is stressed that images generated by iterated function systems can be downloaded or uploaded with less downtime in networking environment with only the mathematical equations which can take less memory. The following chapter presents a new method for generating a class of fractals associating the axioms and productions of classical fractals with a mathematical series represented in L-System. Besides other issues, the authors present the results of testing of the possible combinations of the axiom and rules used for the Koch curve with that of axiom and rules for the recursive mathematical formulae in L-system formats. This was done with a turtle interpreted software for generating a new hybrid class of fractals. The aim of the fifth chapter is to provide a theoretical basis for the design of a tree by calculating the equivalent ramification matrix. The importance of L-systems for botanists to simulate the growth and development of plants, and thus to understand better the processes behind some of the complex tree structures found in the nature, is pointed out. The next chapter is devoted to 3D modeling of realistic plants. Various systems are implemented to demonstrate key aspects of a plant modeling system for the use in a three-dimensional real-time environment; for example, practicality of modeling, realism of models produced and the rendering speed. The calculation of the fractal dimension for various fractals (along with those generated through L-systems) is discussed in the seventh chapter. The book is concluded with the discussion of selected applications of L-systems together with ongoing research work and future directions for research progress; the importance of the L-system approach that enables the simulation of almost all fractal graphics concepts is highlighted. The book is supplemented by the color section exemplifying the potential of the presented methods, and three appendices that contain the L-system codes for various figures including variations of the Koch curve, and for the creation of fractals using the concept of a ramification matrix.