A Multi-Wing Chaotic Attractor Generated via Julia Fractal Process in a New 3D Chaotic System

This paper introduces a novel three-dimensional chaotic system with minimal algebraic complexity, combining hyperbolic tangent and absolute value nonlinearities in only five terms. Despite its structural simplicity, the system exhibits rich chaotic dynamics verified by positive Lyapunov exponents and fractional Kaplan-Yorke dimension. By applying Julia fractal transformations to the system’s state variables, we generate complex multi-wing chaotic attractors with controllable structure and enhanced topological complexity. The number of wings is directly determined by the polynomial order m, enabling systematic generation of multi-wing configurations. The scaling coefficient k controls spatial extent, while the complex constant Z0 modulates wing symmetry and distribution. The fractal transformation preserves dissipative and chaotic properties while enriching phase space geometry through smooth, analytically defined polynomial mappings. Potential applications include secure communication, chaotic encryption, random number generation, and biomedical signal processing.