Jewels from chaos: A fascinating journey from abstract forms to physical objects.

An intellectual journey that began with the discovery of strange attractors derived from Chua's circuit, their translation into physical shapes by means of 3D printers, and finally, to the production of jewelry is presented. After giving the mathematical characteristics of Chua's circuit, we explain the chaotic design process, used for creating jewels, providing specifications of the used methodological approach, for its reproduction. We discuss the feasibility of this approach and the transmission of scientific contents on chaos theory, usually restricted to university students, in a high school Science, Technology, Engineering, Art, and Mathematics course, for the realization of advanced educational processes, implemented both in computational and real environments. We think that the idea of transforming science into art forms can drive students in acquiring scientific knowledge and skills, allowing them to discover the inner beauty of chaos.

SARS-CoV-2 emerging complexity and global dynamics.

The novel SARS-CoV-2 virus, prone to variation when interacting with spatially extended ecosystems and within hosts, can be considered a complex dynamic system. Therefore, it behaves creating several space-time manifestations of its dynamics. However, these physical manifestations in nature have not yet been fully disclosed or understood. Here we show 4D and 2D space-time patterns of the rate of infected individuals on a global scale, giving quantitative measures of transitions between different dynamical behaviors. By slicing the spatiotemporal patterns, we found manifestations of the virus behavior, such as cluster formation and bifurcation. Furthermore, by analyzing morphogenesis processes by entropy, we have been able to detect the virus phase transitions, typical of adaptive biological systems. Our results for the first time describe the virus patterning behavior processes all over the world, giving them quantitative measures. We know that the outcomes of this work are still partial and more advanced analyses of the virus behavior in nature are necessary. However, we think that the set of methods implemented can provide significant advantages to better analyze the viral behavior in the approach of system biology, thus expanding knowledge and improving pandemic problem solving.

On the temporal spreading of the SARS-CoV-2.

The behaviour of SARS-CoV-2 virus is certainly one of the most challenging in contemporary world. Although the mathematical modelling of the virus has made relevant contributions, the unpredictable behaviour of the virus is still not fully understood. To identify some aspects of the virus elusive behaviour, we focused on the temporal characteristics of its course. We have analysed the latency trends the virus has realized worldwide, the outbreak of the hot spots, and the decreasing trends of the pandemic. We found that the spatio-temporal pandemic dynamics shows a complex behaviour. As with physical systems, these changes in the pandemic's course, which we have called transitional stages of contagion, highlight shared characteristics in many countries. The main results of this work is that the pandemic progression rhythms have been clearly identified for each country, providing the processes and the stages at which the virus develops, thus giving important information on the activation of containment and control measures.