Scale Free / Nested Hierarchies

Complex systems tend to be self-similar across scales, observing power-law distributions in their patterning. Further these systems are built up of nested sub-systems, which themselves may be complex systems.

One of the 'fingerprints' of Complex Systems is their tendency to self-organize into power-law distributions. Hence populations of cities, word frequency distributions, values of stocks, and popularity of websites follow regular mathematical patterns. The Emerg. of mathematical regularities is one of the key aspects of CAS that has been studied at length by researchers, who remain intrigued by the ubiquity of these Power Laws across disparate systems.

Power-law distributions in CAS  are no doubt generated in part due to the  Non-Linear dynamics that govern CAS. In these dynamics, as more agents are added to the system, there is a tendency for new Agents to gravitate towards regimes that are already populated with existing agents, in a process known as Preferential Attachment. In effect, this means this means that rich individuals tend to get richer, high valued stocks tend to attract more buyers, and popular websites tend to attract more traffic. While the ubiquity of Power-law distributions in CAS phenomena can almost be described as 'spooky', they are therefore nonetheless a natural outcome of the dynamics governing the systems. 

Once these topological regularities of CAS appear, they are significant not only due to their inherent beauty as patterns per say, but also because of how these patterns channel Information Theory flows through optimizing distribution systems (though Fractals are certainly visually striking on their own). 

Further efficiencies in Complex Systems are achieved when agents aggregate and partition into 'nested hierarchies'.  By partitioning into nested hierarchies agents are able to preserve robustness even if part of the system is damaged. This concept was outlined in depth by {{herbert-simon}} HANDLEBAR FAIL in his seminal article 'The Architecture of Complexity'. The appearance of such nested hierarchies can also follow Power Laws (as noted by Zipf and Pareto ). Power-law distributions specific to urban settings have been studied at length by Bettencourt and West.




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Explore Scale Free / Nested Hierarchies further in the topics and collections below.

Self-Organized Criticality

Power Laws

Fractals

Emerg. of mathematical regularities

Parents

Scale Free / Nested Hierarchies is part of the following collections.

Emerg. of mathematical regularities

Power Laws

CAS Defining Features

Fractals

Self-Organized Criticality


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These are elements and topics related to Scale Free / Nested Hierarchies.

Self-Organized Criticality

Caramelization half and half robust kopi-luwak, brewed, foam affogato grounds extraction plunger pot, bar single shot froth eu shop latte et, chicory, steamed seasonal grounds dark organic. See {{network-topology}} Learn More about Self-Organized Criticality →


Power Laws

CAS tend to self-organize to a critical state, where the distributions of agents relative to their impact on the system follows a power-law distribution. Learn More about Power Laws →


Fractals

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Emerg. of mathematical regularities

What one could describe as the 'fingerprint' of a complex system is the emergence of certain kinds of mathematical regularities that describe the system. Characteristic features of the system are organized according to POWER-LAW Distributions. Power-law distributions also appear in FRACTAL systems. Keep exploring in the topics below to learn more about mathematical regularities in CAS. Learn More about Emerg. of mathematical regularities →


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