This free software is an explorer for Mandelbrot and Julia Sets, with various features such as region saving, suggested colour schemes, and automatic zoom. It allows users to randomly explore fractals with a maximum magnification of 10^13.

First of all, the program lets you save the regions you're exploring, as well as the results of your calculations. You can even export the data to CSV, which is great if you want to analyze it in another program.
In addition to this, the software comes with a range of color schemes that you can use to enhance your experience. You can also use the layer-based editor to modify your images in more detail.
One of the coolest features of this program is the ability to save a sequence of images that zoom out from any starting point. This can be a great way to create stunning visual effects that capture the essence of these fractals.
If you're feeling adventurous, you can even explore the fractals at random, letting the program choose the area to zoom in on next. And if you're wondering just how far you can zoom in, the answer is pretty far – up to a maximum magnification of 10^13.
Overall, this software is a great tool for anyone who wants to delve into the exciting world of fractals. There are many other features that I haven't even mentioned here, so be sure to check out the website for all the details.
Version 3.4:
Added CSV export
Disabled (temporarily) Zazzle integration feature
Disabled Adobe Kuler, as API disabled upstream
Updated Facebook integration to use latest Facebook API
Other minor UI improvements