Rule, Rupture, and Recoverability: Continuum as an Operational Concept in Practice-Based Geometric Abstraction

This article develops Continuum as an operational concept from a practice-based exhibition, CONTINUUM|この世界を構成するもの (The Constitutive Elements of the World), held at the Pola Museum of Art (2021–2022). Through analysis of Hilbert curve, 2021, Incomplete continuum, and Drawing for composition 01–03, it defines Continuum as a structural condition in which a generative rule remains legible across rupture, displacement, or medium transformation. The method is research through art, based on exhibition documentation and structural analysis of the works. The concept is specified by three necessary conditions: a finitely describable generative rule, the survival of that rule across rupture, and its recoverability from structurally adequate incompletion. This recoverability is named the disclosure thesis and framed phenomenologically, rather than as a causal claim about visual cognition. A focused comparison with Hilbert’s space-filling curve clarifies how finite-stage figures can disclose recursive rules, while distinguishing mathematical incompletion from deliberate terminal incompletion in art. Comparison with LeWitt, Albers, the modernist grid, and Molnar situates the framework historically and clarifies its distinctiveness. The article establishes Continuum as a transferable framework for analysing geometric abstraction in which incompleteness functions not as defect but as the condition through which rule, relation, and continuity become perceptible.