Self-organization

Phospholipid bilayer

Water crystals forming on glass demonstrate an emergent natural process occurring under appropriate conditions of temperature and humidity.

Ripple patterns in a sand dune created by wind or water is an example of an emergent structure in nature.

Giant's Causeway in Northern Ireland is an example of a complex emergent structure created by natural processes

Self-organization is a process where some form of order arises out of a random system. The process is spontaneous: it happens on its own. It is not directed or controlled by any agent inside or outside the system.

Self-organization occurs in a variety of physical, chemical, biological, social and cognitive systems. A common example is crystallization. An example from biological chemistry is the lipid bilayer, which is the basis of the cell membrane, and so is of great importance.

Many self-organising things have properties which are "emergent". What this means is that one can't predict what will happen, usually because the possibilities are too many to study. Some examples:

1. Protein folding: after RNA translation, proteins fold themselves up into their working shape. For every protein there are one or two shapes which are stable, but it is almost impossible to predict the folding from the sequence of amino acids.
2. Liberal economic theory argues that free market economies create a spontaneous order, "a more efficient allocation of societal resources than any design could achieve". Friedrich Hayek.
   This is the concept of the "invisible hand" (Adam Smith in The Wealth of Nations). By acting on information with greater detail and accuracy than is possible for any centralized authority, a more efficient economy is created to the benefit of the whole society.