Pick a famous location and the camera will fly you there.
Rendering
Navigation
Controls
ClickZoom in 2×
Right ClickShow orbit
Dbl ClickZoom in 4×
DragPan view
ScrollSmooth zoom
Shift+ClickZoom out
PinchTouch zoom
ArrowsPan (canvas focused)
+ / −Zoom in / out
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 1030× — far beyond
what ordinary floating-point arithmetic allows — by switching to perturbation theory for deep zooms.
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.
Perturbation Deep Zoom
Past 10¹² zoom, 64-bit floats can no longer tell neighboring pixels apart. The explorer then computes one reference orbit in high-precision arithmetic and iterates each pixel's tiny difference from it — unlocking zooms to 10³⁰×.
Orbit Visualization
Right-click any point to see its orbit — the actual path z takes as the formula is iterated. Points inside the set trace bounded loops; points outside spiral away to infinity.
Mandelbrot Set Explorer — Interactive Fractal Zoom with Guided Tour, Julia Set Mode and Perturbation Deep Zoom
The Mandelbrot Set Explorer lets users interactively navigate the intricately detailed boundary of the Mandelbrot set, one of the most famous fractals in mathematics. Click anywhere to zoom in, drag to pan, and discover self-similar structures at any level of magnification. Multiple color themes are available to render the escape-time values with different visual palettes, and a guided tour flies the camera to famous locations such as Seahorse Valley, Elephant Valley, the Feigenbaum point, and miniature copies of the whole set, with a short explanation of the mathematics at each stop.
The computation runs in parallel Web Workers to keep the UI responsive, and deep zooms beyond the limits of 64-bit floating point are rendered with perturbation theory against a high-precision reference orbit, supporting magnifications up to 10^30. The explorer also features a Julia Set mode — pick any point c in the Mandelbrot plane and render the corresponding Julia set — plus an orbit visualization that draws the actual iteration path of z = z² + c for any point you right-click. The rendering algorithm uses the standard escape-time iteration over the complex plane with smooth logarithmic coloring.
Keywords: Mandelbrot set explorer, interactive fractal zoom, deep zoom perturbation theory, guided fractal tour, Julia set visualization, complex number fractals, fractal geometry browser, escape time algorithm, Web Worker fractal rendering, mathematical visualization, orbit visualization, fractal color themes