HoloAttractor: Holomorphic Flow-Based Chaotic Attractor Synthesis via Multi-Format Negative Feedback

HoloAttractor introduces a novel framework for synthesizing chaotic attractors through holomorphic flow dynamics combined with multi-format negative feedback mechanisms. The system explores the intersection of complex analysis, dynamical systems theory, and generative synthesis, demonstrating that holomorphic mappings in the complex plane can produce rich chaotic behavior when subjected to carefully designed negative feedback in multiple signal formats (amplitude, phase, and spectral domains). This work presents mathematical foundations, algorithmic implementations, and experimental results showing emergent attractor geometries with fractal dimensionality. The framework has applications in creative coding, scientific visualization, and the study of complex dynamical systems. Source code and implementation details are provided for reproducibility.