An IFS-based method for modelling horns, seashells and other natural forms

This paper presents a new method of modelling natural forms such as horns, seashells and beaks by means of iterated function systems (IFSs). The characteristic feature of these forms is that one can divide them into parts (called modules) similar to each other in the geometric sense. Starting from a description of the growth process, appropriate transformations are defined, which make it possible to generate sequences of three-dimensional sets. Consequently, a model consisting of modules is obtained. Using accurate transformations results in a precise arrangement of modules in space. It is possible to apply a similarity transformation to a single module or to whole groups, which simplifies and speeds up the modelling process. The way the modules are defined leads to great freedom in modelling, which is confirmed by the presented examples. Therefore the method is more efficient than the hitherto existing methods.