Polynomiography

Polynomiography is the algorithmic visualization of polynomial equations for aesthetic, mathematical, and educational purposes. It is a nascent technique for polynomial root-finding with potential application in art, mathematics, and education.

The concept of Polynomiography arose out of a problem concerning polynomial root-finding in the 1990s by Bahman Kalantari. Kalantari became interested in polynomial root-finding when he was designing masters’ questions for an exam, related to approximations of the square root of two. As he delved deeper into the matter, his interest was piqued at the possibility of generating computer visualizations of the root-finding process. Images thus generated would be related to fractals, but distinct in that the former affords more control over the design than the latter. Additionally, a polynomiography image, called a polynomiograph, does not necessarily exhibit fractal patterns.

Non-fractal polynomiograph of the polynomial ${\displaystyle p(z)=z^{3}-1}$

Newton fractal for three degree-3 roots ${\displaystyle p(z)=z^{3}-1}$ coloured by root reached

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