Here's a really cool input that lets you create textures, patterns, or really crazy brushes based on a pattern you define in a grid form. In some sense you can think of this as a bump map of the actual texture-- the ridges are sharp and pick up the paint, and the valleys are shallow and create transparent areas. However, this analogy only works for opacity and lightness; other settings like radius, jitter and color are just cool to play around with. How does it work? It's pretty simple; it takes your X (or Y) coordinate and performs a modulo operation to get a number that "wraps around". For X,Y coordinates 300,310 with a scale factor of 2^8, you'd have values 44 and 54 (300 % 256 and 310 % 256). Whatever scale factor you use it will be scaled to a range of 0-256 so that we can have a consistent range for our brush settings control.
This gives you a basic "canvas" texture that is pretty predictable (opacity):
With the scale factor you can make the pattern bigger or smaller to suite your brush and painting dimensions, etc.
Finally here are some real examples. You can get some very crazy and interesting brushes. It is pretty fun to add several surface maps controlling radius, opacity, etc, and see what kind of patterns emerge when scribbling a large area.