2D Mandelbrot: Orbit-Trap & Buddhabrot Explorer (2D)

Rendering mode

Orbit trap

Trap shape

Max iterations 250

Trap sharpness 3.0

Every pixel is iterated normally (z = z² + c), but instead of colouring by escape time, it is coloured by the closest distance the whole orbit ever came to the trap shape. This lights up structure both inside and outside the set — a different picture from any escape-time renderer.

Buddhabrot

Colour mode

Max iterations 1000

Samples / frame 4000

Trajectories plotted

Samples tried

Instead of colouring pixels by their own fate, this mode fires millions of random points c, keeps only the ones whose orbit escapes, and plots every step of that orbit's path into a density histogram. The image is statistical, not per-pixel — it needs time to accumulate, and gets sharper the longer it runs.

View

Centre Re

-0.5

Centre Im

0.0

Zoom

1×

How it works

Both modes iterate the same rule, z(n+1) = z(n)² + c, but neither one colours by "how many steps until escape" the way a standard Mandelbrot renderer does.

Orbit trap:   track min(distance(z_n, trap)) over the whole orbit
Buddhabrot:   pick random c, run the orbit, if it escapes plot
              EVERY z_n it visited into a shared histogram

Orbit-trap reveals filaments and rings that escape-time colouring hides completely, because it responds to near-misses with a shape, not to escape speed.
Buddhabrot is not a per-pixel calculation at all — a pixel's brightness is "how many escaping orbits, from anywhere in the sampling region, happened to pass through here," which is why it needs continuous random sampling to converge instead of a single pass.
Zooming or panning changes what each mode plots: the orbit-trap image is recomputed at the new scale, and the Buddhabrot histogram is cleared and rebuilt because the pixel grid it bins into has moved.

-0.5, 0.0 · 1×