Structured Recursive Geometry of Color: Vesica Diffraction, Domain Transforms, and Resonant Selection

This repository presents a conceptual and mathematical exploration of color as an emergent, structurally selected phenomenon, rather than a primitive defined solely by wavelength. The work is developed within the framework of Structured Recursive Geometry (SRG) and focuses on how geometric overlap, diffraction, dispersion, and perception preserve structural identity across multiple transformation domains. The central object of study is the vesica piscis, treated not as symbolic geometry but as the minimal overlap structure capable of generating stable harmonic signatures. By analyzing vesica-based apertures under classical Fourier diffraction, geometry-modulated VP-Fourier transforms, and recursive Fourier mappings, the work demonstrates how certain interference carriers and ratios persist through the full optical pipeline: geometry → frequency → angle → spectrum → perception This persistence is formalized through recursive attractors, fixed-point phase locking, and domain-cycling (Möbius-type) transformations, yielding a small set of stability parameters that govern convergence and structural survival. The accompanying acousto-optic material is included not as a device proposal, but as an exploratory indication that dynamic media and resonant modulation may act as selection operators for light, analogous to how geometric overlap selects harmonics. This highlights a conceptual distinction between reflection/refraction and recursive selection, without asserting engineering feasibility. Key contributions include: A unified geometric interpretation of diffraction, dispersion, and color formation Introduction of vesica-modulated spectral bases (VP-Fourier) Recursive stability analysis and attractor behavior A domain-invariant view of perceptual color structure A symbolic and perceptual extension via recursive glyphs This work is intentionally theoretical and exploratory. It does not propose hardware, experimental apparatus, or immediate applications. Its purpose is to provide a transparent, versioned framework for reasoning about how geometry, medium, and recursion jointly constrain optical and perceptual outcomes. All mathematical derivations, assumptions, and conceptual steps are made explicit to support scrutiny, reuse, or selective adoption by readers interested in optics, geometry-driven modeling, perception, or speculative toy models of structure-preserving transformations.