I've just released Fractor, a free Mandelbrot fractal explorer app for Android. It generates images quickly, and the touch navigation makes it easy to control. It also makes rather splendid wallpapers.
The high speed is possible because of the use of OpenGL for the computationally intensive work of calculating the colour of each pixel. Typically this is done by the phone's CPU, but Fractor offloads it to the GPU. Some phones have more powerful GPUs than others, so you can choose to reduce the resolution of the image whilst zooming to ensure the animation remains smooth. Another option you can set is the maximum iterations. A high number results in a more intricate image, but will also slow down the drawing.
Any nice fractal locations you find can be set as wallpaper or saved as a png image. The images are saved in the Fractor folder in your gallery.If you have an Android phone then I hope you give it a try. If you have an iPhone will this be the App to convince you to switch?