If you're the kind of person who's fascinated by geometric patterns then perhaps you should invest in a program such as Pocket Fracatals.
The app allows you to produce the kind of shapes that aren't possible using classical Euclidian geometry. It does this by using patterns that repeat themselves at smaller scales that can be manipulated by zooming, changing gradients or physically moving them.
Although there are no instructions built into Pocket Fractals, it's pretty easy to start creating shapes thanks to a clearly-labelled interface and toolbar. You simply need to determine the colours, gradients and levels of detail by tapping the appropriate boxes.
Although it's fun for about 5 minutes, this is ultimately a program for people who are really interested in geometric patterns and mathematics, because for mere mortals it gets a little boring after a while.
If you're a geometry boffin or a psychedela fan, it's worth downloading Pocket Fractals.