Asymmetry, Symmetry and Beauty

Abstract

Asymmetry and symmetry coexist in natural and human processes. The vital role of symmetry in art has been well demonstrated. This article highlights the complementary role of asymmetry. Further we show that the interaction of asymmetric action (recursion) and symmetric opposition (sinusoidal waves) are instrumental in generating creative features (relatively low entropy, temporal complexity, novelty (less recurrence in the data than in randomized copies and complex frequency composition). These features define Bios, a pattern found in musical compositions and in poetry, except for recurrence instead of novelty. Bios is a common pattern in many natural and human processes (quantum processes, the expansion of the universe, gravitational waves, cosmic microwave background radiation, DNA, physiological processes, animal and human populations, and economic time series). The reduction in entropy is significant, as it reveals creativity and contradicts the standard claim of unavoidable decay towards disorder. Artistic creations capture fundamental features of the world.

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

“…Personality and creativity (Eisenman and Rappaport, 1967;Arnheim, 1969;Cook and Furnham, 2012) have been identified as two such variables, and highly creative individuals may have a stronger tendency to prefer asymmetrical objects, especially when these exhibit high levels of complexity, as in the case of fractal objects with multiple rotational symmetries, for example. As pointed out previously (Sabatelli et al, 2010), symmetry and asymmetry coexist in many natural and human processes, and the critical role of symmetry in art has been well demonstrated; the complementary role of asymmetry maybe less . Fractal objects offer new perspectives for research on complementary aspects of symmetry and asymmetry in processes of increasing complexity, including processes of visual perception.…”

“…Symmetry directly determines aesthetic preferences and the subjectively perceived beauty of two-dimensional visual images and patterns (Eisenman, 1967;Berlyne, 1971;Jacobsen et al, 2002Jacobsen et al, , 2003Jacobsen et al, , 2006Tinio & Leder, 2009), and symmetrical visual patterns are also more easily remembered and recognized (Deregowski, 1971(Deregowski, , 1972Kayert & Wagemans, 2009) compared with asymmetrical ones. Sabatelli et al (2010) suggested that natural and artistic creative processes rely on common, possibly fractal, transformations. Fractal transformations may describe iterative transitions from simplicity and order (symmetry) to complexity and chaos (asymmetry).…”

Investigation of Bifurcations in the Process Equation

“…Bios is a rare type of organization containing the ability of creation and physiological regulation [2,27]. It is proposed as a mathematical pattern that is a variation of chaos and identified in heartbeat intervals [1,6,18].…”

Comparative Analysis of the Life-Cycle Cost of Robot Substitution: A Case of Automobile Welding Production in China

“…It is widely considered that space-time symmetry is ubiquitous in the universe, and there are lots of symmetric problems waiting to be discovered and studied in every field [18]. To contribute to filling the gap above, taking inspiration from the symmetry philosophy in manufacturing systems engineering, this study further examines the LCC of robot substitution and presents a comparative analysis of the LCC of robot substitution.…”