A power law is the description for a variable which scales with the following function.

This mathematical function has many interesting properties but for now we will simply describe the mathematical function and interesting cases where this function is observed.

As observed by the last equation power laws will look linear in log-log axes. Many real world systems follow a power law but a famous example is that of the Gutenberg-Richter law in earthquakes. The following plot shows a histogram of earthquake data from 1970 to 2014 gathered by the US Geological Survey. There are deviations as seen in the initial roll off of small magnitude events but one does observe power law scaling for events larger than a 5.0 in the Richter scale. In this case the exponent tau is measured to be around one.

What is interesting is how common such power laws can turn up in unexpected places. Reddit uses...