# 8: Self-organized criticality

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

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 Chapter 4.4 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.

The code for this chapter is in chap08.ipynb in the repository for this book. More information about working with the code is in Section 0.3.

This page titled 8: Self-organized criticality is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Allen B. Downey (Green Tea Press) .