So when do we call a system self-organizing?

Recently, in a PhD seminar talk the discussion arose, if a particular system is self-organizing or not. Such discussions are emerging with high probability every now and then followed by a discussion that lasts for some time.
It seems that the term "self-organizing system" is a very difficult concept for the following reasons:
First, being named self-organizing, such system are often literally understood as some entity that organizes itself, like a person managing her own affairs in life. The "self" can be misleading here since it may be understood as a single controlling entity.
Actually in self-organization, there is no "self" that organizes. It rather means that systems appear to organize themselves without external direction, manipulation, or control.

Cloth of gold cone: visible pattern as a result
of a self-organizing process (Image: Wikipedia)

To avoid this misinterpretation, the term is sometimes replaced or augmented with spontaneous pattern emergence. But this creates a mental image of patterns in the reader's mind (like the cone displayed to the right). Other self-organizing processes like coherent laser light or clock synchronization create internal order, but no visible pattern.
Another problem is that you can change a system with external control to one without by redrawing the systems boundaries. So a bunch of workers being instructed by a foreman would not be perceived as self-organizing, but a construction cite with different teams, each one coming with a foreman, but otherwise loosely interacting might be seen as self-organizing (unless you model in the blueprints).
Gershenson and Heylighen proposed a nice way out of this dilemma by stating "self-organization is a way of observing systems, not an absolute class of systems". So depending if the self-organizing view is beneficial, you should model your system accordingly, otherwise not.
Another difficulty arises from the fact that self-organization roots in several disciplines, there are many notions and definitions from biology, chemistry, computer science, cybernetics, economics, mathematics, physics, and sociology. Most of these disciplines contribute one or more definitions on self-organization based on the discipline-specific terminology.
As shown by the following examples, there is no single brief but comprehensive definition for self-organization. The following definitions may be useful though:

A self-organizing system (SOS) consists of a set of entities that obtains an emerging global system behavior via local interactions without centralized control.
(from Research Days'08, see [IWSOS:2008]))

Self-organization is the process where a structure or pattern appears in a system without a central authority or external element imposing it through planning. (Wikipedia)

A self-organizing system is a system that changes its basic structure as a function of its experience and environment. (Farley and Clark 1954)

Are they really refering to the same thing? So be warned, when a discussion heads towards the definition of self-organization!

• C. Gershenson, F. Heylighen. When Can we Call a System Self-organizing? In Banzhaf, W, T. Christaller, P. Dittrich, J. T. Kim, and J. Ziegler, Advances in Artificial Life, 7th European Conference, ECAL 2003, Dortmund, Germany, pp. 606-614. LNAI 2801. Springer.
  
• W. Elmenreich, H. de Meer. Self-organizing networked systems for technical applications: A discussion on open issues. In J.P.G. Sterbenz. K.A. Hummel, editor, Proceedings of the Third International Workshop on Self-Organizing Systems, pages 1–9. Springer Verlag, 2008.