Take a polynomial p(z) of degree 100, where
z ∈ ℂ. Now color every point z
of the complex plane by the argument (the angle) of p(z).
The result has a beautiful property: the zeros of p are
exactly the points where the full color cycle closes on itself.
Each of the 100 roots drifts slowly along its own tiny circular orbit. Individually,
each root just wiggles. But the phase field is globally sensitive — a small displacement
of a single root reshapes the color flow far away from it, because
arg(p(z)) is a sum of contributions from every root.
This is a GPU-accelerated re-implementation as a real-time WebGL shader. Scroll to zoom
into the fractal vein structure. Click anywhere to gently shuffle the root positions and
watch the entire field reorganize.
Inspired by
Simone Conradi, Ph.D.
— originally made with numpy + matplotlib in a marimo notebook.
Re-implemented as a real-time shader by
GenieForge.
