Emergence in artificial life by Gershenson, C. (2021)

Artificial life, Emergence
(Gershenson 2021)


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.


  1. . . "Emergence in Artificial Life". Arxiv:2105.03216 [physics]. http://arxiv.org/abs/2105.03216.
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