ITERATED FUNCTION SYSTEMS FOR OBJECT GENERATION AND RENDERING
Huw Jones · International Journal of Bifurcation and Chaos · 2001
Iterated function systems (IFS) have been used since the mid 1980s in generating fractal forms and in image compression. They have the property of encoding complex structures as relatively simple and concise algorithms and data sets. The complete information for generation of an IFS structure, known as an "attractor", is held in the definition of a few transformation functions, typically affine transformations described by simple linear equations. These transform 2D or 3D objects by combinations of translation, scaling and rotation, preserving parallel lines. The process of generating an attractor using either of the two standard methods is straightforward, but the inverse problem of identifying the IFS for a particular attractor is more difficult. The paper introduces and reviews the uses of Iterated Function Systems, particularly for 2D image and 3D object generation. As well as a general exposition of the method, results developed by the author for creation of fractal objects are shown. Some are based on regular geometric structures, others mimic a number of naturally occurring forms. These deviate from normal practice in using nonaffine transformations in the IFS definition. A new method for synthesising images of smooth objects using IFS is developed and illustrated as an alternative to standard 3D rendering methods (see the cover picture), which are briefly described.