One of the classical examples of power-law distributions may be found in geology. It is the Gutenberg-Richeter law, which relates the number of earthquakes to their magnitude. Mathematically this relation is expressed as \( \lg N = a - b M \). Here \( N \) is a number of earthquakes of certain magnitude \( M \) or stronger, \( b \) is empirically determined and depends on seismic activity of the region, while \( a = \lg N_0 \).

In this text we will briefly present self-organized criticality model, which reproduces the power-law distribution of earthquakes - Olami-Feder-Christensen model.

q-Gaussian distribution is rather interesting generalization of the well-known Gaussian distribution. This generalization arises from the generalized, non-extensive, statistical mechanics, which was proposed by C. Tsallis two decades ago. Despite the fact twenty years have passed there is no simple physical model reproducing the q-Gaussian distribution. But our colleague Julius Ruseckas recently proposed one [1]. In this text we will briefly discuss his "correlated spin" model and will present two related interactive applets.

Herfindahl-Hirschman index (or HHI) describing how close the market is to monopolistic market. This tool is used by organizations responsible for the supervision of fair competition (e.g., when considering corporate mergers). This index is obtained using known market shares, \( s_i \in (0,1] \), of competitors in the market

Ideas present in Thomas Pikkety's book "Capital in the Twenty-First Century" has shaken up the world this summer and now apparently the economic inequality is viewed as a serious problem. But until recently it was a problem interesting only to a few scientists and couple enlightened people. Nick Hanauer was one of the more well-known people who talked about this problem "before it was cool". We invite you to listen to his talk recorded for TED website.

Sierpinski triangle is a fractal named after Polish mathematician Waclaw Sierpinski, who was the first one to describe it in scientific literature (in 1915). The fractal itself is interesting in a sense that it is a two dimensional attractor to couple iterative operations related to triangles (primarily).

In this text we will discuss iterative removal of triangles, shrinking and duplication, chaos game. We will also briefly mention Lindenmayer system, cellular automata and Pascal's triangles.