Digital organisms are computer programs that self-replicate, mutate and adapt by natural selection. They offer an opportunity to test generalizations about living systems that may extend beyond the organic life that biologists usually study. Here we have generated two classes of digital organism: simple programs selected solely for rapid replication, and complex programs selected to perform mathematical operations that accelerate replication through a set of defined 'metabolic' rewards. To examine the differences in their genetic architecture, we introduced millions of single and multiple mutations into each organism and measured the effects on the organism's fitness. The complex organisms are more robust than the simple ones with respect to the average effects of single mutations. Interactions among mutations are common and usually yield higher fitness than predicted from the component mutations assuming multiplicative effects; such interactions are especially important in the complex organisms. Frequent interactions among mutations have also been seen in bacteria, fungi and fruitflies. Our findings support the view that interactions are a general feature of genetic systems.