To see why, stand on the carpet – but choose one with a pile that is not too deep (you might in any case want a vacuum cleaner to hand) – take a bag of rice, pull the top of the packet wide open … and chuck the contents straight into the air. Your aim is to eject the whole lot skyward in one jolt. Let the rice rain down.
What you have done is create a chance distribution of rice grains over the carpet. Observe the way the rice is scattered. One thing the grains have probably not done is fall evenly. There are thin patches here, thicker ones there and, every so often, a much larger and distinct pile of rice: it has clustered.
Wherever cases of cancer bunch, people demand an explanation. With rice, they would see exactly the same sort of pattern, but does it need an explanation? Imagine each grain of rice as a cancer case falling across the country. The example shows that clustering, as the result of chance alone, is to be expected. The truly weird result would be if the rice had spread itself in a smooth, regular layer. Similarly, the genuinely odd pattern of illness would be an even distribution of cases across the population.