Think Complexity, 2nd Edition

Chapter 8. Self-Organized Criticality

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 “Heavy-Tailed Distributions” and pink noise, which I’ll explain 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 I’ll present a sand pile model that was the first system shown to exhibit SOC.

Critical Systems

Many critical systems demonstrate common behaviors:

• Fractal geometry: For example, freezing water tends to form fractal patterns, including snowflakes and other crystal structures. Fractals are characterized by self-similarity; that is, parts of the pattern are similar to scaled copies of the whole.

• Heavy-tailed distributions of some physical quantities: For example, in freezing water the distribution of crystal sizes is characterized by a power law.

• Variations in time that exhibit pink noise: complex signals can be decomposed into their frequency components. ...