INTERACTIVE AND PREDICTABLE MODELLING OF NATURAL FORMS GENERATED BY ITERATED FUNCTION SYSTEMS
Keywords:
Iterated Function System, Natural Fractal, Software Application, Interactive ModellingAbstract
Natural objects are often poorly described by classical Euclidean geometry. Fractals, characterised by fragmented and highly irregular structures, provide an effective mathematical framework for representing natural forms. Fractals are commonly generated using iterated function systems (IFS), defined as sets of contractive mappings on a complete metric space, which guarantee the existence of a unique fixed-point (attractor), typically exhibiting fractal properties. In this work, we present a method for affine transformations of fractals, implemented in an interactive software application. The proposed approach enables intuitive and predictable design by directly manipulating predefined control points via click-and-drag operations. The effectiveness of the method and functionalities embedded in the software application are demonstrated through a case study of nature-like fractals, including a maple tree, a maple leaf, a seahorse, and the Barnsley fern. This case study also provides a review of selected articles on the modelling of fractals in which the author has been involved.References
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