Anyone who has sat and studied a spider's web for a moment or two knows that nature has some admirable skill when it comes to creating interesting patterns. In fact, a lot of manmade structures and artistic designs are based on natural patterns. Finding patterns is easy--they seem to be everywhere--and shooting and collecting photos of them is a fun pastime.
Patterns range from very formal, like the spirals in a chambered nautilus shell (a pattern design that has fascinated artists and scientists for centuries), to very random, like the patterns of frost on a cold windshield. Some patterns are even predictable--like the concentric circles you get when you toss a pebble into a pond. A lot of natural patterns, of course, have important purposes and are used by as identification tools: to help us (and other bugs) to identify one bug from another. In fact, nature relies heavily on patterns to help categorize and organize the plant and animal worlds.
The trick to making strong photos of natural patterns is to isolate them--to fill the frame with just the pattern. That's a relatively easy task with shots like the mud cracks (shot at a botanical garden in Corpus Christi, Texas), but it's a tougher one when you're trying to photograph smaller patterns like those on a bug's back. To capture smaller patterns effectively you'll need to switch to a close-up mode (with a point-and-shoot camera) or, with a DSLR, to use a macro lens (and possibly even extension tubes or a bellows attachment). Some patterns too are very ephemeral in nature--like the bands of color in a rainbow--and capturing them is largely a matter of luck and timing.
Think about natural patterns the next time you're out hiking or even just gardening in the back yard. And remember that the best way to reveal the pattern is to exclude everything else.