Measuring the Complexity of Continuous Distributions

TL;DR

This paper extends measures of complexity, emergence, and self-organization to continuous distributions using differential entropy, enabling the analysis of complex phenomena with known distributions like Gaussian and scale-free types.

Contribution

It introduces a method to quantify complexity in continuous distributions, linking it to information adaptation and broadening applicability.

Findings

Gaussian and scale-free distributions show high complexity values

Complexity measures relate to information adaptation

Method applicable to various continuous phenomena

Abstract

We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We find that a broad range of common parameters found in Gaussian and scale-free distributions present high complexity values. We also explore the relationship between our measure of complexity and information adaptation.