Generation of new batik floral patterns via chaotic modulation and Julia-Mandelbrot fractal transformations

This paper presents a novel hierarchical approach for generating complex floral patterns through sequential application of chaotic modulation and fractal transformations. Classical geometric floral patterns are first subjected to binary chaotic modulation using signals extracted from a four-dimensional memristor-based hyperchaotic system, introducing controlled irregularity into regular structures. Subsequently, Julia and Mandelbrot set-based fractal transformations embed hierarchical self-similarity within these chaotically modulated configurations. The choice of the hyperchaotic system is motivated by its minimal complexity enabling practical analog and digital implementation, hyperchaotic dynamics providing rich modulation signals, and capability to generate multi-scroll attractors. Analysis demonstrates that global geometric order coexists with local fractal complexity in the resulting patterns, with topological features and symmetries partially preserved throughout the transformation cascade. This synergistic synthesis of chaotic dynamics and fractal geometry opens new possibilities for generating patterns with tunable visual and topological characteristics applicable to digital art and textile design.