The old example of the change in phase states: water is solid when frozen, gravitational (equilibrious) when liquid, and chaotic when steam.

Except that when it is steam it closely follows the law of ideal gases and is, therefore, a rather simple system with no structure.

If you want chaos and structure you have to look at the critical point.

At the critical point, the scattering is so intense that the system becomes opaque. This phenomenon is called critical opalescence. The domains demonstrate some interesting properties, such as fractal shapes, and there is a peak in the heat capacity. This critical transition temperature is a maximum with respect to the composition. Thus it can be determined by interpolating transition temperatures from known compositions.

Interesting stuff happens not deep in the phases, but on the phase boundaries.

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes