The Visual Stability Problem

Visual environments increasingly exhibit high element density, configurational heterogeneity, and functional layering, challenging limited attentional capacity across sequential fixations. We formulate the Visual Stability Problem as sustaining coherent perceptual organization across entire visual fields under sequential viewing. Stability is operationally defined by three measurable outcomes: consistent attentional anchoring (fixation cluster variance), structured inter-element transitions (scanpath entropy), and interpretable spatial relationships (judgment accuracy). We distinguish structural stability (stimulus-driven) from cognitive stability (task-dependent) to isolate invariant stimulus properties. Three interdependent necessary mechanisms are identified: attentional anchoring establishes spatial reference coordinates, directional guidance constrains transition probabilities, and spatial distribution bounds the global solution space. Crucially, we propose a task-dependent, non-linear density–performance function wherein task type moderates effect magnitude and direction. Reframing visual organization as global coherence rather than local saliency computation, this work provides a testable framework for eye-tracking validation and graph-theoretic modeling of attentional networks, positioning visual stability as a measurable structural property. Keywords: Visual stability, perceptual organization, visual attention, eye-tracking, scanpath entropy, spatial structure, information visualization, cognitive science, human–computer interaction