Figure 2.

Measuring string complexity. If ℓ(p) is the length of the program, the Kolmogorov complexity K(x) is defined as the smallest program able to write x. Simple dynamical systems (a) such as oscillators produce predictable, simple strings (b) thus having a low complexity. On the other extreme (c), a coin toss creates a completely random sequence and the program (d) is such that K(x) = ℓ(x). A system exhibiting broad distributions (e–f) and a large set of states is also likely to display high K(x).