In a recent paper (at the time of writing, in review in Nature), we needed to remind the reader of the little known fact that the aggregation of multiple distributions over a range of scales reliably produces a power law distribution—a special type of distribution that has no well defined scale, or variance [1, 2]. The figure we came up with looks something like this:
The part of the aggregation (right panel) which forms a straight line, is exactly a power-law. To make this relation very clear I made an Observable notebook (which got featured in Explorables!) where one can play with different parameters and types of distributions.