new icn messageflickr-free-ic3d pan white
Algebraic numbers glow dust | by Jonathan Lidbeck
Back to photostream

Algebraic numbers glow dust

Using WebGL for realtime approximation. See it live: www.glslsandbox.com/e#42524.0

 

An aggregation of the complex roots of

 

0 = a₀ + a₁z + a₂z² + a₃z³ + a₄z⁴ + a₅z⁵ + a₆z⁶ + a₇z⁷ + a₈z⁸

 

where a₀ = 1 and a₁...a₈ = 1 or 0.

 

Rather than computing the roots, this is an implicit plot, taking advantage of GPU parallelism. The polynomials are evaluated at each pixel and sets brightness for values near zero, indicating proximity to a root.

 

The brightest points lie on the unit circle, representing various roots of unity: -1, ±i, (1±i√3) / 2, etc. Note that +1 (at right) is dark, as no positive real roots exist for this set of polynomials.

 

Different colors are assigned according to the coefficients of the first and second powers of z.

1,392 views
2 faves
0 comments
Uploaded on September 18, 2017