Mandelbrot Set Explorer
Explore the Mandelbrot set — the boundary of the set of complex numbers c for which the iteration z → z² + c stays bounded. The renderer maps each pixel to a complex number c, iterates until |z| exceeds a bailout radius or hits a max-iteration limit, and colors by escape time. Click to recenter, scroll or use the buttons to zoom, and switch to a Julia set for a chosen c. Because the set is self-similar at every scale, you can zoom essentially forever (limited by double-precision arithmetic). Everything runs locally in your browser.
Click on the image to recenter there. Drag is not required — click to recenter, then zoom.
Selected point
The Mandelbrot set M is the set of complex numbers c for which the sequence z₀ = 0, zₙ₊₁ = zₙ² + c remains bounded (never escapes to infinity). The renderer uses the standard escape-time test: iterate up to maxit steps; if |zₙ| ever exceeds a bailout radius of 2 the point escapes (and is outside M), colored by how fast it escaped (smooth iteration count gives banding-free color); if it never escapes within the limit it's treated as inside (black). The bailout radius of 2 is sufficient because once |z| > 2 the orbit provably escapes. A Julia set uses the same iteration but with a fixed c and varying starting z — each Mandelbrot point c corresponds to a Julia set, and points inside the Mandelbrot set yield connected (filled-in) Julia sets. Pairs with the Function Plotter, Spirograph, and Monte Carlo tools. Everything runs locally — nothing leaves your browser.