Abstract
Beauty judgments for regular polygon tessellations were examined in two experiments. In experiment 1 we tested the three regular and eight semi-regular tilings characterized by a single vertex. In experiment 2 we tested the 20 demi-regular tilings containing two vertices. Observers viewed the tessellations at different random orientations inside a circular aperture and rated them using a numeric 1–7 scale. The data from the first experiment show a peak in preference for tiles with two types of polygons and for five polygons around a vertex. Triangles were liked more than other geometric shapes. The results from the second experiment demonstrate a preference for tessellations with a greater number of different kinds of polygons in the overall pattern and for tiles with the greatest difference in the number of polygons between the two vertices. Ratings were higher for tiles with circular arrangements of elements and lower for those with linear arrangements. Symmetry group p6m was liked the most and groups cmm and pmm were liked the least. Taken as a whole the results suggest a preference for complexity and variety in terms of both vertex qualities and symmetric transformations. Observers were sensitive to both the underlying mathematical properties of the patterns as well as their emergent organization.
Highlights
We outline the different types of tessellations, showing that they can be categorized by the types of polygons they contain, the way they are arranged around defining vertices, and their symmetry properties
Beauty ratings were normalized by the formula of/(max − min) where the minimum and maximum were determined across subjects
There was a significant effect of Polygons in Pattern, F(2, 93) = 114.03, p < 0.01, with peak responding found for tilings with two polygons (Figure 2)
Summary
These can be seen in the tiles on floors, in wallpaper patterns on our walls, and in the clothes we wear. They are found in decorative artwork that adorns the outside of buildings and in signs, advertising, and in graphic and web design [1]. We will examine these questions by looking at a group of tessellations, known as tilings, whose geometric and mathematical properties are well defined. We will use these properties to predict and help explain their aesthetic appeal. We outline the different types of tessellations, showing that they can be categorized by the types of polygons they contain, the way they are arranged around defining vertices, and their symmetry properties
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