- tags
- Artificial life, Emergence
- source
- (Gershenson 2021)
Summary
The paper introduces a complexity metric based on information. emergence is first measured with Shannon’s information: \[E = - K \sum_{i} p_i \log p_i\]
Then the author argues that self-organization can be seen as the opposite of emergence, and measured with \[S = 1 - E\]
[…] complex systems tend to exhibit both emergence and self-organization. Extreme emergence implies chaos, while extreme self-organization implies immutability. Complexity requires a balance between both emergence and self-organization.
Therefore we can measure complexity as: \[C = 4 S \cdot E\] where \(S\) and \(E\) have been normalized to \([0, 1]\). It is noted that the metric corresponds to phase transitions in several complex systems (citations omitted in quote):
This measure \(C\) of complexity is maximal at phase transitions in random Boolean networks, the Ising model, and other dynamical systems characterized by criticality.
Bibliography
- Gershenson, Carlos. April 30, 2021. "Emergence in Artificial Life". arXiv:2105.03216 [Physics]. http://arxiv.org/abs/2105.03216.