Polynomial roots visualisation inspired by 2swap's video on the quintic (github.com)

An innovative C application that visualizes polynomial roots in the complex plane has been developed, drawing inspiration from 2swap's captivating video on the quintic formula. This interactive tool allows users to manipulate polynomial coefficients and observe the dynamic behavior of roots, offering a comprehensive exploration of polynomial transformations. Two primary modes enable users to focus on either the roots of polynomials or their coefficients, with additional "cloud mode" for generating diverse polynomial combinations. Significantly, the application leverages advanced computational techniques, including OpenCL for GPU rendering and LAPACK for efficient root-finding, allowing for smooth visual interactions even during complex calculations. The use of temporal coherence to estimate root positions during user manipulations minimizes computational load, enabling real-time performance. Furthermore, the application supports customizable animations via JSON scripts, enhancing user engagement with polynomial behaviors. This project underscores the fusion of mathematical theory with visual technology, making polynomial concepts more accessible and engaging for the AI/ML community and beyond.