For each point in the famous Mandelbrot set fractal, there is a unique Julia set fractal parametrised by that point. Mandelbrot Maps is a fractal viewer designed to demonstrate the relationship between the two by generating the relevant Julia fractal in real-time as you move a pin across the Mandelbrot set.
Move around the fractals by dragging with one finger and pinch with two to zoom in and out. Hold your finger down to drop a pin and explore the Julia set. If you find a particularly beautiful spot, you can save the image or share it with friends.
Mandelbrot Maps is open-source software - you can find the source on my GitHub account, which is linked on this page as the developer website.
If you enjoyed using this version of Mandelbrot Maps, you might want to try Fractal Maps by Sky Welch, an updated version with improved speed and a side-by-side view - https://play.google.com/store/apps/details?id=io.bunnies.fractalmaps.
Chris King has also produced a version (not currently on the Play Store) that adds several more kinds of fractal - http://www.dhushara.com/DarkHeart/MM/MandelbrotMaps.htm.
This Android port of Mandelbrot Maps is based on the original web app created by Iain Parris (http://homepages.inf.ed.ac.uk/wadler/mandelbrot-maps/mmaps.html, http://www.inf.ed.ac.uk/publications/thesis/online/IM080583.pdf) and further developed by Edward Mallia (http://edwardmallia.com/mandelbrotmaps/), and Taige Liu. All versions were done under the supervision of Philip Wadler (http://homepages.inf.ed.ac.uk/wadler/) at the University of Edinburgh.