As this small sample shows, a random distribution of cases will almost always be clumped.
Some Random Distributions
Only a regular distribution, which is unlikely to occur without some external force, shows no clumping.
A Regular Distribution
If you are interested, you can set the number of dots and generate some random distributions, to get a feel for what they look like.
A further cause of clustering in this case is that population is itself already highly clustered. Thus, we should be less surprised by an aggregation of leukemia in a densely settled area like Woburn, than we would be by an aggregation in northwestern Montana.
If you are interested, you can set the number of dots and generate some random distributions over an already clumped substrate, to get a feel for what such distributions might look like.
