Polynomiogram: An Integrated Framework for Root Visualization and Generative Art
Hoang Duc Nguyen, Anh Van Pham, Hien D. Nguyen

TL;DR
Polynomiogram is a versatile computational framework that combines scientific analysis and artistic generation of polynomial root visualizations, supporting research, education, and creative expression.
Contribution
It introduces a flexible sampling scheme and dual numerical engines, enabling both high-precision scientific validation and efficient artistic visualization of polynomial roots.
Findings
Validated numerical accuracy with classical polynomial ensembles
Analyzed bifurcation structures in cubic systems
Generated personalized artistic visualizations
Abstract
This work presents the Polynomiogram framework, an integrated computational platform for exploring, visualizing, and generating art from polynomial root systems. The main innovation is a flexible sampling scheme in which two independent parameters are drawn from user defined domains and mapped to the polynomial coefficients through a generating function. This design allows the same mathematical foundation to support both scientific investigation and generative algorithmic art. The framework integrates two complementary numerical engines: NumPy companion matrix solver for fast, large scale computation and MPSolve for high precision, scientifically rigorous validation. This dual architecture enables efficient visualization for creative use and accurate computation for research and education. Numerical accuracy was verified using classical ensembles, including the Kac and Lucas…
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Taxonomy
TopicsPolynomial and algebraic computation · Music Technology and Sound Studies · Aesthetic Perception and Analysis
