This tutorial makes use of Inkscape (www.inkscape.org), an open-source vector graphics editor. I imagine that this method can be applied to expensive vector graphics programs like Adobe Illustrator as well. Hey, it's your money.
Step 1: Set Up the Document
First, change the width and height of the document to a number that is easier to work with. For this tutorial, I created a square image, but any proportion will do.
Next, you'll want to set up the grid. In older versions of Inkscape, there was only one grid possble. In newer versions, you'll need to create a new grid. Change the grid spacing so that these values divide evenly into the values of the document width & hegiht.
Generally, it's a good idea to work from a large image and then scale down as necessary. Because this is vector art, size techincally does not matter, but practically speaking, it will be easier conceptually with larger numbers. In this tutorial, I used a 500x500px image, and my grid is at 10px intervals.
Finally, make sure that the "Enable snapping" option is checked.
Step 2: Rectangle Tool
Step 3: Cloning the Pattern
Create a clone of this image. ([Edit -> Clone -> Create clone] or you can press Alt+D)
Move the original image out of the way so that won't interfere with your workspace.
Move the cloned image into the square, and create a few copies of the clone. The reason for using clones instead of copies of the origina will become apparent later.
Here's an easy way to make copies in inkspace: drag the object to be copied, and press the spacebar to drop a copy at that spot (keep the mouse button depressed).
Generaly, you probably don't need more than 2 or 3 copies to create the pattern. As you can see, I had 3 copies of the image but I ended up deleting one later. Once you think you have enough, group these items together.
Step 4: More Cloning
Select the group of objects you just created, and make a clone of that group.
Line up the edges of the clone with the page border, and keep dropping copies of the clone until you have at least a 3x3 grid of clones around the original in the middle.
Step 5: Expert Movers
To move objects that are inside a group, the most straight-forward method would be to first ungroup the objects, move the object in question, and then re-group the objects. However, this will break the links to the clones.
Instead, we want to keep the group intact while manipulating single objects within the group. To do this, hold the Control button and click on the object you want to modify. Control-click selects single objects within a group.
If you now move the objects, the surrounding clones will also reflect the change. Using this method, you can now move the images around until you are satisfied with your overall pattern. You can also resize, rotate, or delete the images. I ended up deleting one of the images because I only needed 2 to fulfil the pattern.
Step 6: About Using Cloned Images
Step 7: Finishing Touches
I also decreased the opacity of the group as a whole (select by regular click) so that the pattern can be in the background and not be intrusive.
Finally, the important step of exporting. Open up the exporting window ([File -> Export bitmap]). Click the "Page" button. This will export just the parts of the document that fall within the page boundaries -- that is, inside the square of the "original".
Change the exported bitmap size if you want, and then click "Export".