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Geometrical Possibilities of the Modern Architectural Morphogenesis

Innovative architectural forms arise and develop at the intersection of science and art, architecture and engineering. Architecture and design have become the areas of practical application of mathematical concepts of spatial fragmentation. The approaches used in the classical geometry and “new” non-Euclidean geometries can be applied to a certain extent to the development of the spatial potential of architecture and urban planning. This particular work is related to various scientific areas, including geoinformatics, biology, crystallography, engineering geometry and computer modeling. The interdisciplinary approach allows us to reveal the spectrum of new geometric shapes, as well as patterns for space-filling and fragmentation of a two-dimensional surface and three-dimensional space. The study is of a theoretical nature, although the results can be applied in educational practice and experimental design. Keywords—morphogenesis and architectural geometry; architectural and landscape urbanism; morphogenesis of nature; innovative and virtual architecture; computer modeling; spatial