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EXPLORER 03 / INFINITE POSSIBILITIESA little closer
A little closer
to infinity.
zn+1 = zn² + c
One simple rule. An endless world.
Follow your curiosity into the Mandelbrot set.
AN INFINITE COASTLINE1×
Drawing your first view…
Drag to wander · Double-click to zoom · Shift + scroll to zoomz₀ = 0
YOUR POINT IN THE COMPLEX PLANE
A FEW PLACES TO BEGIN
Take the scenic route.
Somewhere extraordinary is one click away.
A SMALL RULE, A BIG IDEA
When does a number escape?
Start at zero. Square it, add a complex number c, and repeat. Some points stay bounded; others race away. Color reveals how quickly each point escapes. Dark points haven’t escaped within your detail limit, so a higher limit may reveal more.
Zoom along the boundary to find spirals, branching shapes, and miniature worlds. The set is infinitely detailed; this canvas uses finite precision and a maximum magnification of 10¹⁰×.