Three root basins of z³−1 fill the plane with gold, cyan and violet.
Newton's method applied to f(z) = z³ − 1 divides the complex plane into three fractal basins, one for each cube root of unity. The boundaries between basins are infinitely intricate — a Julia set in disguise. This classic view shows all three basins at once, a vivid demonstration of how a simple root-finding algorithm produces unexpected fractal geometry.
Real axis (Re)
0
Imaginary axis (Im)
0i
Zoom
1.5×
Max iterations
60
Complex address
A classic Mandelbrot region filled with curling seahorse-like spirals.
Mandelbrot SetMassive elephant-trunk filaments wind through the boundary in repeating arcs.
Mandelbrot SetA dense spiral basin where bifurcating arms fold into one another.
Mandelbrot SetSnowflake-like dendrites flare around a dark bay in cool ocean tones.
This is just one of thousands of unique views. Open the interactive explorer and find your own.
