Fractal Explorer is a sample application to illustrate how to use Robospice for a non-network related background task. Here, we used a fractal as an example of a long running background task.

Pinch, zoom and move inside a Mandelbrot fractal computed in an Android service...

https://github.com/octo-online/robospice

RoboSpice has been designed to perform network requests asynchronously. This app demonstrates it can also be used in "offline" mode for tasks not related to the network.