Newton Fractal Basins

Newton's method on the complex plane. Each pixel's color shows which root it converges to; brightness encodes iteration count. Boundaries are fractal — every boundary point is a Julia set.

Polynomial: z³ − 1 = 0 z⁴ − 1 = 0 z⁵ − 1 = 0 z⁴ − z = 0 z³ − 2z + 2 = 0 Max iterations: 60 Color mode: By root By iteration count Smooth shading Render

Click + drag to zoom | Newton fractal