The laws of thermodynamics are just that: laws; edicts on how participants in a system behave. In emergence, we discussed how a simple set of rules for individuals can combine to produce cumulative effects on groups of elements within a system.

The concept of self-organization is discretely different, asserting that collective order can arise from small-scale interactions between individuals. In this way, self-organizing systems contain an internal logic that provokes individuals to combine to form coherent shapes or achieve a functional purpose beyond that which an individual can achieve.

From the internal rules of a self-organizing system, collective behaviors can emerge.

In general, 4 principles guide self-organizing systems:

1) Positive feedback

2) Negative Feedback

3) Dynamic balance between the creation and consumption of resources

4) A Plurality of Participants


It may not be obvious at this point and in fact it has been contended to me that, indeed, I have not made this point clearly enough. In a universe such as ours, the rules for self-organization are laid out in the rules of thermodynamics and the principle of order.

As such, much as the pursuit of equilibrium is an emergent behavior of a non-equilibrium system expanding through nothingness, the Fibonacci sequence too is an emergent behavior of a system seeking equilibrium; a pattern inspired by the constraints of conservation of energy, the 2nd law of thermodynamics and the pursuit of equilibrium.


Thermodynamics, Number Theory and The Goilden Ratio
Creation, Evolution and the Golden Rule
Theory of Order
Why Fibonacci and Gibonacci sequences appear everywhere in nature,
and how simple combinatoric math can describe how a Universe with simple beginnings evolved into a complex form