Scientists from the Budapest Technological University have made a groundbreaking discovery of a new type of form, known as “soft cells” or “Z cells”. This discovery could hold the key to unraveling how mathematical concepts are manifested in nature. The unique characteristic of these soft cells lies in their curved edges and the absence of sharp corners, setting them apart from traditional geometric shapes. The findings of the study were recently published on arxiv, showcasing how these forms can be interconnected in both two- and three-dimensional space without the usual mathematical constraints imposed by corners and edges.
For centuries, mathematicians have focused on exploring figures structured with clear lines and sharp angles, investigating their capacity for infinite connections. However, this new discovery highlights nature’s inclination towards softer and more fluid forms. The study emphasizes that one of the central challenges in geometry is to fill space with simple structures.
Conventional solutions such as triangles, squares, and hexagons on a plane, as well as cubes and other polyhedra in three-dimensional space, are typically constructed using sharp corners and flat faces. In contrast, natural forms often feature curved edges and non-flat surfaces, prompting a reevaluation of the relationship between theoretical and natural forms.
Researchers assert that they have successfully addressed this challenge by identifying an “infinite class of multifaceted fillings” that can be transformed into soft forms, creating soft versions of cells typically associated with point lattices in two and three dimensions.
The lead author of the study, Gabor Domokosh, highlights the presence of these soft forms not only in art but also in biology. For instance, microscopic examination of muscle tissue cross-sections reveals cells with only two acute angles, presenting a distinctive illustration of such fillings.
Furthermore, the study showcases how the shells of mollusks serve as a natural manifestation of this form. Mollusk shells are known to be composed of multiple chambers, with their growth following a pattern that can be adjusted. Through three-dimensional measurements of shells using a computer tomograph, the research team observed the absence of sharp angles, despite variations in the appearance of the two-dimensional shell. This revelation underscores nature’s divergence from our current geometric understanding and paves the way for further exploration of forms in the natural world.