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Open AccessArticle

Affine Geometry, Visual Sensation, and Preference for Symmetry of Things in a Thing

ICube Laboratory UMR 7357 CNRS, University of Strasbourg, Strasbourg 67000, France
Academic Editor: Marco Bertamini
Symmetry 2016, 8(11), 127;
Received: 4 August 2016 / Revised: 15 October 2016 / Accepted: 9 November 2016 / Published: 14 November 2016
(This article belongs to the Special Issue Symmetry in Vision)
Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of symmetry is controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion. View Full-Text
Keywords: visual symmetry; affine projection; fractals; visual sensation; aesthetics; preference visual symmetry; affine projection; fractals; visual sensation; aesthetics; preference
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Dresp-Langley, B. Affine Geometry, Visual Sensation, and Preference for Symmetry of Things in a Thing. Symmetry 2016, 8, 127.

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