Theoretical Principle of Self-Suppression of the External Space of an Expanding Shape: Dynamic Folding Modeling Applied to a Square

This article proposes a novel theoretical principle according to which a closed geometric shape in expansion can suppress its own external space through an internal mechanism, without the intervention of external constraints. Unlike classical approaches where growth is limited by imposed boundaries, we explore here a dynamic folding of the shape’s edges. Using a visual analogy—each side of a square represented by two arms of a fictitious character facing outward—we show that the coordinated folding of these arms can lead to the complete absorption of the surrounding space. This self-closing process renders any further expansion impossible. This hypothesis, conceptual in nature and not formally demonstrated, invites a reconsideration of the notions of limits, expansion, and saturation in geometric systems. It could provide a theoretical basis for exploratory models in cosmology, morphogenesis, theoretical mathematics, spatial computing, or autonomous artificial intelligence. We have presented here a conceptual principle based on a simple analogy, according to which a geometric shape can, through an internal folding, suppress its own external space. Although this is not a formal proof, this hypothesis opens a new field of reflection on the dynamics of closed forms, the redefinition of boundaries, and the intrinsic expansion limits of systems. Contrary to classical approaches where growth is limited by obstacles or externally imposed boundaries, this model relies on the idea of an internal spatial absorption mechanism. Applied to all sides of a square, this process leads to complete saturation: the external space is absorbed, making any further expansion impossible. By proposing a closure that is not imposed but self-produced, this model calls for a re-examination of geometric growth, emphasizing the role of internal transformations in defining spatial structure. It also lays the foundation for an interdisciplinary discussion on the possibility of autonomous, self-regulated expansion systems. Moreover, this dynamic folding principle is not limited to the square: it can be applied to any closed shape—rectangles, triangles, circles, spheres, or others—provided that an internal contact space allows the triggering of the folding mechanism. Finally, this theoretical modeling can be seen as a basis for reflection on larger-scale systems, notably cosmological ones. It suggests that even an entity as vast as the universe, considered as an expanding form, could theoretically contain within itself the conditions for an internal folding capable of defining or imposing an absolute limit.