Mandelbrot Explorer

Explore the parameter plane

Each pixel is c in z→z²+c, starting at z0=0. Choose an iteration budget and Render preview. The parameter belongs to the mathematical Mandelbrot set only if the critical orbit remains bounded forever. A finite budget cannot certify every dark pixel; higher iterations may reveal late escape. Colour uses finite-cutoff double-log smoothing rather than a measured potential.

Navigation and Julia handoff

Drag pans, pinch or Ctrl/Meta-wheel zooms. Ordinary wheel scrolls the page. View coordinates expose centre/half-width with equal axis scales. Reset redraws the initial window. Right-click resets, copies coordinates, changes palettes or opens Julia with c equal to the clicked parameter in a new tab. Julia pixels then represent initial z while its c remains fixed.

Export and limits

Preview and export calculate in short cancellable pixel batches with real progress. PNG has independent dimensions/iterations; it preserves exact raster size and embeds UTF-8 mode/window/palette/phase/budget parameters. Export settings preserve the old preview, parameter edits invalidate it. Double precision limits deep zoom; half-width below1e−14, collapsed/overflowing views and exports over8192 per side/50 million pixels are rejected instead of silently altered. Palettes may also be dark outside the set. All computation is browser-local; saved valid state restores without autorender.

The upper toolbar holds the main controls and PNG action. View coordinates, colour phase and PNG resolution are optional details. Typed values, including unfinished numeric drafts, remain on reentry. Mouse/touch zoom and panning are temporary; no rendered raster is saved.

Selecting a named region immediately calculates its actual pixels, with the current iteration budget and Cancel available. The Julia action uses exactly the clicked parameter c, but opens a fitted whole-set view around z=0 rather than reusing the Mandelbrot zoom. Changing the palette during calculation restarts with the new colours.

Named regions fit their reference square into the shorter image dimension, so a wide monitor does not cut off the main bulb. Manually entered view coordinates and half-width remain exact.