This is the real, standard 2D Mandelbrot set: for every pixel c in the complex plane, z starts at 0 and is repeatedly updated by z → zn + c. If |z| ever exceeds a bailout radius the point has "escaped" and is colored by how quickly that happened, using smooth continuous coloring; points that survive the full iteration budget are considered inside the set and painted near-black. With n=2 this is the classic Mandelbrot set; sliding the power exponent produces the related family of Multibrot sets. The 3D Mandelbulb takes this same power-n idea and applies it to spherical coordinates in three dimensions — this page is its 2D parent.
A true escape-time fractal computed per pixel with real complex-number iteration, not an approximation — z_{n+1} = z_n^n + c tested against a large bailout radius, with a smooth normalized escape count driving the color.
Drag to pan, scroll or pinch to zoom into the boundary. Power n reshapes the set (n=2 is the classic Mandelbrot, higher n gives Multibrot variants with more lobes). Max iterations trades fine boundary detail for speed. Reset view returns to the default framing.
The 3D Mandelbulb has no true complex-multiplication analogue, so it reuses this same power-n exponent idea in spherical coordinates (r→r^n, θ→nθ, φ→nφ). This page is the 2D original that generalization is built from.