FRACTAL APPROACHES IN DIGITAL TIME VISUALIZATION TECHNOLOGIES DURING 3D MODELING OF ASTRONOMICAL EQUIPMENT

Abstract

Based on theoretical and empirical research, it has been determined that in the context of time and its visualization, fractals help to reflect complex, multi-level processes that repeat on different time scales. In the process of 3D modeling, it is possible to simulate cyclical and self-similar time changes (sunrise-sunset, seasonal changes), to use fractal algorithms to generate complex but predictable changes in shadows and light. When modeling astronomical equipment (sundials, telescopes, planetariums, etc.), fractal approaches help to develop structures that distribute or direct light as accurately as possible. The article focuses on 3D modeling in the process of manufacturing homemade astronomical equipment, namely a sundial. It has been established that a digital sundial is a modern interpretation of a traditional sundial, which, instead of a simple shadow position, shows time in the form of real digital digits, as on an electronic display. The following sequence of 3D modeling is proposed: creating a set of coordinates for the location of each digit according to the position of the Sun at a certain time; creating a base volume in the form of an inclined 3D platform; forming small protrusions or holes (a kind of 3D pixels) that either block or transmit light; creating 3D digits, each of which (0-9) is divided into fragments (pixels) that will cast the correct shadow at the appropriate time; superimposing all positions into a single model; eliminating unnecessary protrusions that may cast incorrect shadows at other times; modeling the path of the Sun and checking how the digits are projected at different times; exporting the model to *.stl format for 3D printing; 3D printing. It has been established that the integration of the fractal approach into the process of developing astronomical equipment not only expands the boundaries of traditional technical thought, but also forms a new methodology of digital visualization based on mathematical aesthetics. Further research in this direction may consist in creating functional, visually appealing, and educationally meaningful devices that combine accuracy, beauty, and scientific innovation.