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

Birgitta Dresp-Langley

doi:10.3390/sym8110127

Abstract

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 design parameters and shape symmetry for visual or tactile shape sensation, and for perception-based decision making in populations of experts and non-experts. Thereafter, results from a pilot study on the effects of fractal symmetry, referred to herein as the symmetry of things in a thing, on aesthetic judgments and visual preference are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (scale from 0 to 10) the perceived attractiveness 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.

Highlights

Brain evolution has produced highly specialized processes which enable us to effectively exploit the geometry of visual perceptual space
The following paragraphs will expand on the importance of affine geometry, the symmetry of curves, which may be perceived as single things or as multiples of one and the same thing in a complex shape or object [9,10], and visual sensation
In the data from the preference judgment experiment with figure pairs, a first check of the means showed no effect of secondary variables such as the spatial position

Summary

Introduction

Brain evolution has produced highly specialized processes which enable us to effectively exploit the geometry of visual perceptual space. Some data suggest that the human brain is equipped with an in-built sense of geometry [1,2] which provides a key to recognizing specific object properties, associations between two-dimensional projections, and their correlated three-dimensional structures in the real world [3–6]. These associations favour structural regularities and, very often, symmetry [6,7], while asymmetry plays a critical role in processes of perceptual discrimination, as discussed recently regarding music and sounds [8]. In the domain of visual objects, symmetry plays an important role in conceptual processes for structural design, and is abundantly exploited by engineers and architects. Thereafter, two-dimensional fractal trees based on geometrical principles which produce symmetry of things in a thing will be discussed and made use Symmetry 2016, 8, 127; doi:10.3390/sym8110127 www.mdpi.com/journal/symmetry

Methods

Results

Discussion

Conclusion