An engineering blog had this to say about self-organising systems (edited by me to clean up the English and particularise it for here):
Self Organization requires several conditions for it to occur and be observed:Above all this, it must be remembered that the control system has to be at least as complex as the system it is controlling: accommodating entropic loss; somewhat along the lines of an Ashby-Conant regulator.
• A high degree of structure
• The capacity for coordinated action
• A mechanism for system-wide feedback and amplification
• Some means to transform a small event into a larger driving force for the system to organize itself into a coherent system
Primary is coordination across boundaries and the capacity for action. This implies - quite explicitly - a deterministic response to external stimulus. The self-organization properties require structured communication channels for the systems to posses this property.
So next time you hear self organizing as the way evolution works, best ask to see what structures are identified to provide the channels for coordinated actions. What mechanisms are being used for system-wide feedback within that highly structured process framework, and what are the means of transforms small - potentially very small stimuli - into the collective actions of the whole?
In the broader sense, these concepts all live in a world governed in a deterministic manner through...
• Feedback - the return of a portion the output of a process or system to the input. These means modeling the transform function - usually G(S), where S is the system dynamic model, and G is the transform function. Both can be represented by non-linear differential equations
• System Dynamics is the next level of modeling for the structured, coordinated, system-wide feedback and amplification (both positive and negative).
◦ This involves state-space modeling or phase space) where an abstract space - a mathematical model in which all possible states of a system - are represented, with each possible state of the system corresponding to one unique point in the state space. Dimensions of state space represent all relevant parameters of the system. For example state space of mechanical systems has six dimensions and consists of all possible values of position and momentum variables.
◦ The Trajectory of the system describing the sequence of system states as they evolve.
◦ A fixed point in the state space where the system is in equilibrium and does not change. In complex projects and systems they represent, this is the steering signal needed to compare the feedback to so corrective actions can be taken by the system to maintain equilibrium and run off the cliff.
◦ The Attractor is a part of the state space where some trajectories end.
• The actual dynamics of the system - where the set of functions that encode the movement of the system from one point in the state space to another. This is the foundation of the mechanism for feedback and structuring of the disconnected components of the system. These dynamics are many times modeled with sets of differential equations containing the rules for the interactions.
Of course, evolutionary speculation contains none of this detail, or even a sketch of it...
