Pixel Dude is an image editing app for the iPad. Like the name suggests, it's pixel based, and is good for drawing chunky graphics. The drawing area is a 32 by 32 grid of squares, which I find to be more than enough for my purposes.
I've always liked the look of the Space Invaders aliens, and by using Pixel Dude's symmetrical drawing tool, it's very easy to create characters that have that Space Invaders look. The application has a lot of other features, like layer support and unlimited undo and redo.
Once you are done drawing something you can email it or save it to Dropbox.
Eventually, I would like to use these patterns to silkscreen onto t-shirts. Keep an eye out for my how-to project on this!