Complexity is a property of a system. A system is something, which has many parts, whose components interact with each other. A system&...
Complexity is a property of a system. A system is something, which has many parts, whose components interact with each other.
A system's complexity is describable quantitatively by evaluating the following system properties:
- Cardinality: how many parts the system has.
- States: how many different states of the parts of the system can have.
- Connections: how many bonds (either dedicated or non-dedicated) have a component of the system with other components of the system.
- Interactions: how the state of some system components is affected by the state of other system components through connections.
- Channels: what is the bandwidth of the interaction of the connections
Complexity explosion
As multi-component systems evolve, the system becomes more and more complex. The complexity explosion is due because of the connections between the components within the system. Connections create structures within the system. If the structures lead to inhomogeneity in the system, the created structures act as unique components at a new level of complexity. Because the created structures are built from elements with its states of the lower-level system, the higher-level components represent the combined states of the lower-level components, thus the higher-level components can have exponentially more states than the lower-level components. Because the states of the components are determining factor in the complexity of a system, exponentially many states cause the complexity explosion, as the multi-component systems evolve.
Levels of complexity
If a complex system creates an emergent property, the system creates a new level of complexity.
Threshold
A new class of a complex system emerges if the emergent properties of the complex system become related to each other.
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