Complexity, Growth and Aging

We examine the evolution of complexity of a class of dynamical systems having different dimensions and initial densities of the corresponding Complexity Maps. Each system experiences small and randomly injected increments of entropy.

System dimension: 20

Map densities of 1, 0.75, 0.5 and 0.25 are considered.

System dimension: 50

Map densities of 1, 0.75, 0.5 and 0.1 are considered.

The table below provides a synthesis of the results:

An example of decaying structure is shown below.

The Complexity Map at T1 – corresponding to peak complexity – is illustrated below. The map has 258 nodes, 8262 rules and a density of 25%.

In conclusion, in all cases it may be obseved that:

  • There is a phase in which an increase in entropy increases complexity, this is a period of growth.
  • Once peak complexity is reached, a period of decline commences. This is accompanied by loss of structure (Complexity Map density is progressively reduced).
  • Decline continues until complexity is zero.
  • Higher initial density implies that the system may reach higher peak complexity.
  • Lower initial density implies that the system ‘dies’ sooner.
  • In low-density systems decline may be ‘traumatic’, i.e. sudden, accompanied by a large loss of complexity.
  • Higher initial density implies that the system may be more difficult to destroy.

These findings apply to both natural (biological) as well as man-made systems.

Established originally in 2005 in the USA, Ontonix is a technology company headquartered in Como, Italy. The unusual technology and solutions developed by Ontonix focus on countering what most threatens safety, advanced products, critical infrastructures, or IT network security - the rapid growth of complexity. In 2007 the company received recognition by being selected as Gartner's Cool Vendor. What makes Ontonix different from all those companies and research centers who claim to manage complexity is that we have a complexity metric. This means that we MEASURE complexity. We detect anomalies in complex defense systems without using Machine Learning for one very good reason: our clients don’t have the luxury of multiple examples of failures necessary to teach software to recognize them. We identify anomalies without having seen them before. Sometimes, you must get it right the first and only time!

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