In the previous chapter we saw an example of a system with a critical point and we explored one of the common properties of critical systems, fractal geometry.
In this chapter, we explore two other properties of critical systems: heavy-tailed distributions, which we saw in Section 6.5 and pink noise, which We’ll see in this chapter.
These properties are interesting in part because they appear frequently in nature; that is, many natural systems produce fractal-like geometry, heavy-tailed distributions, and pink noise.
This observation raises a natural question: why do so many natural systems have properties of critical systems? A possible answer is self-organized criticality (SOC), which is the tendency of some systems to evolve toward, and stay in, a critical state.
In this chapter We will explore a sand pile model that was the first system shown to exhibit SOC.