Click to zoom. Right-click to save images, M to make and save a movie of your zoom path.
z → z2+c is iterated for each complex number c. Colors show iterations to divergence; black points converge or cycle.
Yellow dots show orbits. Red dots show limit cycles.
About iterations. This viewer shows more fractal detail over time by refining iterations to infinity as you explore. The longer you wait, the more detail is shown. After thousands or millions of iterations, you can resolve the finest details in the most complex parts of the fractal. See information on iterations, progress, and coordinates by hovering over the yellow zoom number under each window. Moving your mouse over fractal content will animate the orbit of z values for each location c, revealing the complex boundary dynamics that have fascinated mathematicians.
Exploring a zoom path. Each click on the fractal opens a higher zoom level at the selected location, computed by a new webworker thread. After you zoom beyond trillion-fold magnification, we slow things down a bit to use a quad-precision perturbation algorithm that resolves fine details to more than 30 digits of accuracy. Once you have crafted an interesting path that shows the detail you want, you can create and download your own Mandelbrot deep zoom video or bookmark your URL to save and share your exploration. To create high-quality images and videos, this viewer computes subpixels with a 2:1 ratio, and that can be increased to create more precise displays.
More commands:
I zooms in;
Ctrl-click to zoom in-place;
H shrinks and G grows each window;
R reopens midway windows;
C recenters all;
T changes color theme;
U highlights unfinished pixels;
Enter toggles full-screen;
X increases and Z decreases the z exponent;
F increases and D decreases the pixel ratio;
M makes a movie that follows your path;