There is a tendency to mistake complexity for randomness. Faced with lots of data, especially when squeezed into a small area, one often has trouble seeing patterns, leading to a presumption of randomness -- when upon careful analysis, distinctive patterns can be recognized.
We encountered this when looking at the "sad tally" of the Golden Gate Bridge suicides (here, here, here, here and here). Robert Kosara's recent work on scribbling maps of zip codes also highlights the hidden patterns behind seemingly random numbers.
Robert found a related example (via Information Aesthetics, originally here): the artist takes random numbers (lottery numbers), and renders them in a highly irrelevant graphical construct, as if to prove that spider webs can be generated randomly.
According to Infosthetics, each color represents a number between 1 and 49, which means the graph contains 49 colored zigzag lines (not counting gridlines and axes). Each point on the year axis represents a frequency of occurrence.
Imagine if you are tasked with using this chart to ascertain the fairness of the lottery, that is, the randomness of the winning numbers. The complexity of this spider web makes a tough job impossible! We must avoid the tendency to jump to the conclusion of randomness based on this non-evidence.
In fact, testing for randomness can be done using any of the methods described in the postings on the "Sad Tally" (links above). A first step will be to plot the frequency of occurrence data as a simple column chart with 1 to 49 on the horizontal axis. We'd like to show that the resulting histogram is flat, on average over all years.