Explore complex fractals

A simple rule, repeated many times, can create surprisingly intricate pictures. These explorers let you change the rule and see what happens, directly in your browser.

Start with Mandelbrot & Julia: right-click the parameter panel and move the mouse, or double-tap and drag on mobile. Watch the picture in the other panel change.

Each explorer has two views. The dynamical plane shows what happens to different starting points for one rule. The parameter plane is a map of different choices of that rule. A complex number is just a point here: its real part runs horizontally and its imaginary part vertically.

Drag to pan and scroll or pinch to zoom; use Reset view if you get lost. More iterations reveal finer structure but take longer to draw. The pictures use your device’s graphics hardware (WebGL).

• Logistic Family

  Explore the complex logistic map and the fate of its critical orbit.

• Mandelbrot & Julia

  Change one complex number to explore the Mandelbrot set and its Julia sets.

• Newton's Fractal

  Find the roots of a polynomial and explore where Newton’s method converges.