Origin

Abstract

This work introduces the Layered Cartesian Stone Strip, a multi-dimensional geometric framework designed for mapping data, space, and dynamic systems with universal reference across layers and transformations. Rooted in the recursive  logic and extended to layered envelopes with square, hexagonal, or triangular cross-sections, this model provides a stable yet flexible structure to visualize and measure relationships in systems of arbitrary complexity.

The core idea is the nesting of twisted spatial tubes each layer representing a logical or physical boundary around a central strip at a stable control angle of 120°, ensuring consistency and directional coherence. Each successive layer scales proportionally, maintaining calculable path lengths and allowing point-to-point, axis-based, and temporal measurements across layers. This enables consistent comparisons of geometry, trigonometry, and calculus-based projections.

The structure supports data mapping, motion tracking, and field analysis by anchoring coordinates in an emergent frame of reference. Applications include trajectory mapping in physical environments (e.g., skydiving through fog), layered data analytics in augmented reality, and universal systems modeling across recursive layers. With the ability to infinitely expand and recursively reference state-layer interactions, this model provides a novel pathway for deterministic spatial computation, emergent logic systems, and unified mapping of reality.