Tool
Multibrot explorer
Family of escape-time sets z ← zn + c for integer n ≥ 2. The standard Mandelbrot is the case n = 2; higher exponents add (n − 1)-fold rotational symmetry.
Click to zoom in (shift-click to zoom out). Drag to pan.0 ms
center: (0.000000, 0.000000)
scale: 3.50e+0
Iteration rule
z_{n+1} = z_n^3 + c with z_0 = 0
in polar form: (r e^{iθ})^3 = r^3 e^{i 3θ}
escape test: stop when |z_n| > 2
rotational symmetry: 2-fold in c-spacen = 2 recovers the classic Mandelbrot. As n grows the set approaches the closed unit disk.
Background at /fractals/multibrot.