Patterns and Swatches in Illustrator
Illustrator comes with a multitude of graphic styles, patterns and swatches as well as the fact you can create your own.
Draw a small square with a sample of what you want the new pattern to be.
Select all of the elements you want in the pattern then drag them onto the swatch toolbar.
You can then make any new shape and apply the new pattern to it. It will automatically be repeated.
If there are white patches, zoom in and look at your pattern close up to make sure all elements line up to the edges.