---
slug: paper-wang-h-et-al-2024-complexity-and-entropy-of-natural-patterns
title: Wang et al. 2024: Complexity and Entropy of Natural Patterns
canonical: https://miscsubjects.com/a/paper-wang-h-et-al-2024-complexity-and-entropy-of-natural-patterns
---

## What the work establishes
Haoyu Wang, Changqing Song, and Peichao Gao published "Complexity and entropy of natural patterns" in PNAS Nexus in 2024. The paper tests the common view that complexity rises then falls during mixing processes while entropy steadily increases. It finds this view is an artifact of how systems are characterized by dimension and resolution.

Core result: when natural patterns are measured with a multi-scale complexity metric from Bagrov et al. (2020) and proper characterization, complexity does not decrease. It aligns statistically with thermodynamic entropy.

## Exact primary works and passages
The paper is Wang, H., Song, C., & Gao, P. (2024). Complexity and entropy of natural patterns. PNAS Nexus, 3(10), pgae417. https://doi.org/10.1093/pnasnexus/pgae417

Key passage from the abstract: "We demonstrate that this consensus is, in fact, an illusion resulting from the choice of system characterization (dimension) and the unit of observation (resolution). By employing a complexity measure designed for natural patterns, we find that the complexity of a coffee-milk system never decreases if the system is appropriately characterized in terms of dimension and resolution. Also, this complexity aligns experimentally and theoretically with entropy."

From the introduction: "In everyday life, there is a common consensus that while entropy never decreases, complexity does decrease after an initial increase during the process of blending coffee and milk."

Significance statement: "Our study uncovers the statistical consistency between complexity and entropy, shedding light on the nature of complexity as a thermodynamically coherent measure of a system."

The work draws on Bagrov et al. (2020) for the complexity measure and Boltzmann entropy formulations.

## Convergence patterns evidenced
The findings link complexity and entropy statistically in natural patterns. This supports scale invariance through multi-scale renormalization and thermodynamic coherence of structures via alignment with entropy measures.

The work touches the GRAIN elements of scale invariance and thermodynamic constraints on structure formation.

## Distance from the full synthesis
The paper stays within empirical measurement of spatial patterns. It reaches the level of statistical consistency between complexity and entropy but does not address the Ladder from difference to mind or the Mirror Layer of observer inclusion. It provides a mechanistic foundation for structural patterns without extending to life or cognition.

## Honest limits and disconfirming edges
Results apply to spatial natural patterns under the chosen measures. They do not prove universality across all complexity definitions. The consistency is statistical, not absolute in every case. Reductionist accounts that treat complexity as observer-dependent remain compatible where characterization choices vary.

No data on biological or cognitive systems. Claims rest on simulated and image-based patterns.

## Claims
The paper shows proper system characterization removes the apparent peak-and-decline in complexity during mixing. Tier: mechanistic. Source: Wang et al. 2024 abstract.

Complexity aligns statistically with thermodynamic entropy under multi-scale measurement. Tier: mechanistic. Source: Wang et al. 2024 significance statement.

Scale and resolution choices determine measured complexity and entropy values. Tier: mechanistic. Source: Wang et al. 2024 abstract.

The work supports thermodynamic coherence of natural patterns. Tier: mechanistic. Source: Wang et al. 2024.

The paper does not address observer inclusion in the system. Tier: unsourced.
