Re: -0.50000000 Im: 0.00000000 Zoom: 1.00× Initializing…

Controls

Fractal Mode

Hover over canvas, then click Julia Set

View

Zoom 1×

Re(center) -0.5

Im(center) 0.0

Rendering

Max Iterations Auto 200

Color Theme

Navigation

Controls

Click Zoom in 2×

Right Click Show orbit

Dbl Click Zoom in 4×

Drag Pan view

Scroll Smooth zoom

Shift+Click Zoom out

Pinch Touch zoom

About the Mandelbrot Set

The Mandelbrot set is one of the most famous objects in mathematics — a fractal defined by iterating the deceptively simple formula z → z² + c in the complex plane. For each complex number c, we repeatedly apply this rule starting from z = 0. If the result stays bounded forever, the point belongs to the set (shown in black). If it eventually escapes to infinity, the point is colored by how quickly it escapes.

No matter how deeply you zoom in, new structure keeps appearing — the same shapes recur at every scale, yet each region has unique character. This explorer supports zoom up to 10¹³×.

Escape Time Algorithm

Each pixel maps to a complex number c. We iterate z = z² + c until |z| > 2 (escaped) or we reach max iterations. The iteration count determines the color.

Smooth Coloring

Smooth (continuous) coloring avoids harsh bands by using a logarithmic formula: iter + 1 − log₂(log₂|z|). This produces silky gradient transitions.

Julia Sets

Each point in the Mandelbrot plane corresponds to a unique Julia Set — a related fractal using the same formula with a fixed c. Toggle Julia mode to explore them.

Web Workers

Pixel computation runs in parallel Web Workers (one per CPU core), keeping the UI responsive. The canvas is split into bands, each computed simultaneously.