Perceived Complexity as Normalized, Integrated, Localized Shannon Entropy.

Overview

1. Department of Biology, Loyola University Chicago, Chicago, IL 60660, USA
2. Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
3. Department of Psychology, Loyola University Chicago, Chicago, IL 60660, USA

Abstract

Perceived complexity is a key component of sensory brain function as it indicates the number of resources necessary to process incoming information. A recently proposed measure of perceived complexity defined it as normalized Shannon entropy. However, the proposal used probability distributions estimated from the entire sensory signal at once. Here, we first used synthetically created images and abstract expressionism art to show that using such distributions seemed incompatible with perceived complexity. This incompatibility persisted even if we performed the calculations at different scales, that is, in multiple image resolutions. We then proposed an alternate theory that postulated that perceived complexity arose from the integration of localized Shannon entropy. The outcome of this integration was then normalized to define an index of complexity. We measured this index and integrated Shannon entropy in 704 images obtained from natural and urban settings, painted by well-known artists, or created synthetically. Moreover, we studied the dependence of these measurements on the spatial scale used to measure Localized Shannon Entropy. We found that normalized, integrated, localized Shannon entropy at low spatial scales is consistent with the phenomenology of perceived complexity and illustrates interesting aesthetic choices of different artists.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Data

Datasets cited

• osf:nwz42, at OSF; found in the text, “3.1. Images”
• sberquet.github.io/perceived-complexity-as-normalized-integrated-local-shannon-entropy, at sberquet.github.io; found in the text, “3.1. Images”

Data Availability Statement

All data are in the Supplementary Materials reported above.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 2 authors, 10 keywords, 2 funders, 112 references.

Cite

This paper

Berquet, S., & Grzywacz, N. M. (2026). Perceived Complexity as Normalized, Integrated, Localized Shannon Entropy. Entropy (Basel, Switzerland), 28(3), 279. https://doi.org/10.3390/e28030279

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