The complexity equation shows how it is possible to measure the intensity of physical processes, which can be categorized as Structure->Entropy and Entropy-> Structure transformations.
What this means is that sometimes structure is turned into chaos or disorder becomes structure. Not surprisingly Nature is full of examples precisely because, at a very high level, it does these two things. Physical processes involve transport of matter, transmission and transformation of energy as well as transmission and processing of information. Some of these processes are illustrated in a recent blog.
In this short blog we illustrate a beautiful animation of ice formation as the temperature of water is lowered (source).
As temperature is lowered (from left to right) more ice crystals form (more structure) and entropy decreases (less disorder). At the same time, as more structure emerges, complexity increases, which is typical of phase transitions from liquid to solid, see plot below:
The full animation is shown below.
Artificial Intuition 
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