This ghostly figure emerges from a simple equation repeated millions of times. No one designed it—it was discovered hiding in pure mathematics.
The Algorithm
Pick a random point c in the complex plane (the starting position)
Iterate the equation: zn+1 = zn2 + c, starting with z0 = 0
Track the orbit—the sequence of points z visits
If the orbit escapes (|z| > 2), record every point it visited
If the orbit stays bounded, discard it (these points are in the Mandelbrot set)
Repeat millions of times and count how often each pixel was visited
Interactive Demo
Click anywhere on the left panel to pick a starting point c. Watch how the orbit (the path) evolves. Only escaping orbits contribute to the final image.
Complex Plane (pick point c)
Click to select a starting point c
Accumulated Hits
Escaping orbits: 0 | Total hits: 0
The Colors (Nebulabrot)
The Nebulabrot variation uses different iteration limits for each color channel, revealing structure at multiple scales:
Short orbits tend to stay near the Mandelbrot set boundary, while long orbits wander further—creating the ethereal, nebula-like appearance.
Why "Buddhabrot"?
The name was coined by Lori Gardi in 1993 when she noticed the figure's resemblance to a seated Buddha in meditation. The shape emerges naturally from the mathematics—a surprising example of order arising from chaos.