Fractal Design Pattern Generation from Non-Affine IFS and Machine Learning-Driven Clustering-Based Segmentation

Abstract

In this paper, we present a novel application of fractals using different Iterated Function Systems (IFS), which employ non-linear transformations for design patterns for garments or for wall or floor interiors. Here we provide a template for the generation of fractal pattern designs using both contractive IFS and non-contractive IFS, relying on the condition that non-contractive IFS produce self-similar attractors under certain circumstances. To segment the intricate patterns generated by IFS into distinct styles, we employ certain clustering techniques in machine learning, such as K-means clustering and self-organizing map (SOM) clustering. Furthermore, to quantitatively measure the pattern's complexity and self-similarity, the fractal dimension of the fractal design pattern is computed via the box-counting method, allowing for a more precise evaluation of the pattern's intricacy and aesthetic appeal. This method of generating fractal pattern designs and segmenting them using machine learning algorithms enables the fashion industry to create innovative designs with minimal programming expertise, even without traditional fashion or artistic skills.