СИМЕТРІЯ В ДИЗАЙНІ ВІЗУАЛЬНИХ КОМУНІКАЦІЙ: СПОСОБИ ПОБУДОВИ ДИНАМІЧНОГО ХУДОЖНЬОГО ОБРАЗУ

The purpose of the study is to reveal methods of image creation in dynamic visual communications based on symmetry. Methodology. Research methodology is interdisciplinary. It is based on systems and synergistical approaches. They consider dynamic visual communications as an integral field of interaction between human and environment. We systematized design methods of the image creation of a visual message by using the system and functional, structural and dynamic, composition, artistic and image design-analyses according to the principles of symmetry. Results. We represent symmetry as a method of dynamic visual communications form and image creation. Symmetrical relations are formed at the object structure level (mirror symmetry and central symmetry), the process level (translational symmetry, multilevel central symmetry and radial symmetry) and environment level (scale invariance and recursion). Integrative basis strengthening allows forming the structure of the image content providing fusion with an environment. Rethinking of the design methods on the based on the principles of symmetry increases the efficiency of perception and visual communications dynamic in the context of changeable external conditions. Scientific novelty. In the research we rethought the role of symmetry in dynamic visual communications design based on the systems approach for the first time. It is well-proven that the symmetric transformations support increasing of aesthetic, functional and communicative qualities of dynamic visual information. Practical significance. Research materials can serve as basis for harmonization and optimization of the form and content of different visual communications types. Their image structurization according to the principles of symmetry provides new development strategies of the integrated visual communications. It is important to increase perception efficiency in the conditions of continuously growing information volumes. Researched design methods of visual communications symmetric structures can be used by specialists in order to arrange the modern space. We also use them as the basis for designers’ system thinking forming as an educational technology.

Planar vector fields with central symmetry: roughness and first degree of non-roughness

Рассматривается пространство гладких векторных полей, заданных в замкнутой области D на плоскости, инвариантных относительно центральной симметрии и трансверсальных границе D. Описано множество векторных полей, грубых относительно этого пространства; показано, что оно открыто и всюду плотно. Во множестве всех негрубых векторных полей выделено открытое всюду плотное подмножество, состоящее из векторных полей первой степени негрубости. We consider the space of smooth vector fields defined in a closed domain D on the plane, invariant under the central symmetry and transversal to the boundary D. The set of vector fields that are rough with respect to this space is described; it is shown that it is open and everywhere dense. In the set of all non-rough vector fields, an open everywhere dense subset consisting of vector fields of the first degree of non-roughness is distinguished.

Students’ understanding of axial and central symmetry

The paper focuses on students’ understanding of the concepts of axial and central symmetries in a plane. Attention is paid to whether students of various ages identify a non-model of an axially symmetrical figure, know that a line segment has two axes of symmetry and a circle has an infinite number of symmetry axes, and are able to construct an image of a given figure in central symmetry. The results presented here were obtained by a quantitative analysis of tests given to nearly 1,500 Czech students, including pre-service mathematics teachers. The paper presents the statistics of the students’ answers, discusses the students’ thought processes and presents some of the students’ original solutions. The data obtained are also analysed with regard to gender differences and to the type of school that students attend. The results show that students have two principal misconceptions: that a rhomboid is an axially symmetrical figure and that a line segment has just one axis of symmetry. Moreover, many of the tested students confused axial and central symmetry. Finally, the possible causes of these errors are considered and recommendations for preventing these errors are given.

Aqueous Solubility of Organic Compounds for Flow Battery Applications: Symmetry and Counter Ion Design to Avoid Low-Solubility Polymorphs

Flow batteries can play an important role as energy storage media in future electricity grids. Organic compounds, based on abundant elements, are appealing alternatives as redox couples for redox flow batteries. The straightforward scalability, the independence of material sources, and the potentially attractive price motivate researchers to investigate this technological area. Four different benzyl-morpholino hydroquinone derivatives were synthesized as potential redox active species. Compounds bearing central symmetry were shown to be about an order of magnitude less soluble in water than isomers without central symmetry. Counter ions also affected solubility. Perchlorate, chlorate, sulfate and phosphate anions were investigated as counter ions. The formations of different polymorphs was observed, showing that their solubility is not a function of their structure. The kinetics of the transformation can give misleading solubility values according to Ostwald’s rule. The unpredictability of both the kinetics and the thermodynamics of the formation of polymorphs is a danger for new organic compounds designed for flow battery applications.

The Fractal Geometry of the Nymphalid Groundplan: Self-Similar Configuration of Color Pattern Symmetry Systems in Butterfly Wings

The nymphalid groundplan is an archetypical color pattern of nymphalid butterflies involving three major symmetry systems and a discal symmetry system, which share the basic morphogenesis unit. Here, the morphological and spatial relationships among these symmetry systems were studied based on cross-species comparisons of nymphalid hindwings. Based on findings in Neope and Symbrenthia, all three major symmetry systems can be expressed as bands, spots, or eyespot-like structures, suggesting equivalence (homology) of these systems in developmental potential. The discal symmetry system can also be expressed as various structures. The discal symmetry system is circularly surrounded by the central symmetry system, which may then be surrounded by the border and basal symmetry systems, based mainly on findings in Agrias, indicating a unified supersymmetry system covering the entire wing. The border symmetry system can occupy the central part of the wing when the central symmetry system is compromised, as seen in Callicore. These results suggest that butterfly color patterns are hierarchically constructed in a self-similar fashion, as the fractal geometry of the nymphalid groundplan. This self-similarity is likely mediated by the serial induction of organizers, and symmetry breaking of the system morphology may be generated by the collision of opposing signals during development.

Game with Central Symmetry on a Rectangular Board

A game with central symmetry on a rectangular board, created with Unity3D, is presented. It is available for both PC and Android with mixed reality. The purpose of creating the game is to provide conditions for the development of digital and mathematical competence in students through play in both formal and non-formal learning. Four options are described, depending on the presence or absence of animation, as well as the limitation of working time.