Zn+1 = Zn2 + C

The Mandelbrot Set is a mathematical curiosity that has fascinated people since it was first discovered in the 1980s. It is a set of complex numbers that, when iterated through the formula above, either remain bounded or escape to infinity. The boundary of the set is the famous fractal image that is so recognizable.

The basic idea on this site is to click somewhere in the image, probably around the border, to zoom in on that spot. On this site, each click doubles the magnification centered at that point. The display is generated on the fly and will provide accurate images for magnifications up to 1012 or so.

As you click through the images, thumbnails of each view are saved at the bottom of the page. Clicking on a thumbnail will return you to that view.

The Reset button returns to the default view, which is the full-size image. All history is lost when you reset.

The Back out button doesn't exactly return to the previous view. It zooms out to a view centered on the same spot as your current view. This is useful if you've found an image you love, but want it centered differently. Back out, and click on a new center to zoom in.

The Perma-link button copies a URL to your current view to your clipboard so you can save it for later or share it with others.

Normal images are 900 x 675 pixels, which is small enough to render reasonably quickly. The Huge button will create an image 3600 x 2700 pixels — big enough to work well for printing or using as a monitor background. Be patient. Your browser will scale it to fit, but you can save it at full "huge" size by dragging it to your desktop, or by right-clicking on it and selecting "Save image as", or whatever the Mac equivalent is. Images with lots of black (including the full-size view) take longer to render.

The Locate button zooms out to the full view and highlights where you are in the full Mandelbrot set. You can then reset to the previous view if you like.

Yes, I realize I'm now the one-millionth programmer to write a Mandelbrot Set viewer. But look how colorful and pretty this one is!

Server: MD17-136