Mutual attraction is a dominant force in the universe. Gravity binds the moon to the earth, the earth to the sun, the sun to the galaxy, and one galaxy to another. And yet the universe is expanding; the result is a larger universe comprised of elements that coalesce into clusters. Human history is much the same – more and more people spreading throughout the world, coupled with increasing urbanization. This map from the UN shows how urbanization is associated with economic development — with the exception of several desert countries that cannot sustain a dispersed population at all, all of the most urbanized countries are also among the most economically developed.
The US illustrates two forms of this mutual attraction force – immigrants coming to the US, and US residents leaving rural areas to live in the city.
A number of different statistical methods are used to analyze and understand the force for mutual attraction. Amazon leverages statistical models to predict what you will like, based on what other people similar to you like. Facebook and LinkedIn built their business models on nourishing and harvesting the networks that people form with each other.
Clustering algorithms have the longest history in this arena, and Vince Granville has built some ingenious computer simulations to model illustrate the tendency of objects to coalesce into clusters – see <http://www.analyticbridge.com/group/codesnippets/forum/topics/simple-solutions-to-make-videos-with-r >
Watching the clusters form is seductive.