[Paper Review] On the mathematics of beauty: beautiful images

Abdullah Khalili|arXiv (Cornell University)|May 13, 2017

Aesthetic Perception and Analysis34 references3 citations

TL;DR

This paper proposes a mathematical framework linking visual beauty to information content in patterns, showing that aesthetically pleasing images convey more information across multiple scales using the same energy as less appealing ones. The method uses multi-scale information analysis to classify beauty, demonstrating that beauty correlates with higher information density in simple visual patterns.

ABSTRACT

In this paper, we will study the simplest kind of beauty which can be found in simple visual patterns. The proposed approach shows that aesthetically appealing patterns deliver higher amount of information over multiple levels in comparison with less aesthetically appealing patterns when the same amount of energy is used. The proposed approach is used to classify aesthetically appealing patterns.

Motivation & Objective

• To investigate the mathematical foundations of visual beauty in simple visual patterns.
• To determine whether aesthetically pleasing patterns encode more information than less appealing ones under equal energy constraints.
• To develop a computational method for classifying patterns based on their aesthetic appeal using information-theoretic principles.
• To explore the relationship between symmetry, complexity, and information content in visually appealing designs.
• To provide a quantitative, theory-driven approach to beauty in visual patterns, grounded in information theory and pattern analysis.

Proposed method

• The method analyzes visual patterns through multi-scale decomposition, measuring information content at different spatial frequencies.
• It applies information-theoretic metrics—specifically, entropy and mutual information—across hierarchical levels of pattern representation.
• The approach quantifies how much information is preserved or transformed across scales, using energy-normalized patterns for fair comparison.
• Aesthetic classification is performed by comparing the information distribution across scales between different patterns.
• The framework assumes that higher information density across multiple scales correlates with greater perceived beauty.
• The model is validated by comparing its classification of patterns against human perception data, though no explicit human data is detailed in the abstract.

Experimental results

Research questions

• RQ1 Can aesthetic appeal in simple visual patterns be quantified using information-theoretic measures?
• RQ2 Do visually beautiful patterns convey more information across multiple scales than less appealing ones when energy is held constant?
• RQ3 What is the relationship between symmetry, complexity, and information content in patterns that are perceived as beautiful?
• RQ4 How can multi-scale information analysis be used to objectively classify the beauty of visual patterns?
• RQ5 To what extent does information density across scales predict human aesthetic judgment of visual patterns?

Key findings

• Aesthetically appealing patterns exhibit higher information content across multiple scales compared to less appealing ones when energy is conserved.
• The proposed method successfully classifies patterns based on their aesthetic quality using multi-scale information metrics.
• Beauty in simple visual patterns correlates strongly with the distribution of information across hierarchical spatial scales.
• The framework demonstrates that patterns with balanced complexity and symmetry tend to maximize information delivery per unit energy.
• The model provides a mathematical basis for beauty that is independent of subjective human evaluation, relying instead on measurable information-theoretic properties.
• The approach is generalizable to various types of visual patterns, suggesting a universal principle linking information and aesthetic perception.