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

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

. . “Emergence in Artificial Life”. arXiv:2105.03216 [Physics], April.

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