TITLE:
When Landscape Becomes Geometry II: Multi-Anchor Fibonacci Spiral Modeling in the Bosnian Valley of the Pyramids
AUTHORS:
Sam Osmanagich, Massimo Guzzinati, Richard Hoyle
KEYWORDS:
Bosnian Valley of the Pyramids, Fibonacci Spiral, Golden Ratio, Spiral Architecture, Landscape Geometry, Pyramid Complexes, Tumuli, Monte Carlo Simulation
JOURNAL NAME:
International Journal of Geosciences,
Vol.17 No.3,
March
31,
2026
ABSTRACT: This study extends prior geometric analysis of the Bosnian Valley of the Pyramids by evaluating Fibonacci-based logarithmic spiral modeling within a fixed geodetic coordinate framework. Using high-resolution LiDAR data and predefined summit-level reference points, spiral trajectories governed by a constant golden-ratio growth factor (φ ≈ 1.618) were applied under bounded scale and orientation parameters. A uniform ±20 m positional tolerance threshold and a minimum three-node intersection criterion were enforced. Formal Monte Carlo testing (10,000 iterations) was conducted for the Sun-anchored configuration under symmetric spatial redistribution with identical parameter constraints. The resulting four-node intersection lies in the upper tail of the simulated distribution, indicating that comparable multi-node coherence occurs infrequently under uniform spatial randomness within the valley envelope. Additional anchor points exhibit descriptive multi-node spiral correspondences under the same modeling framework but were not subjected to independent hypothesis testing. The probability estimates presented are conditional on the defined planar null model and do not incorporate terrain-constrained redistribution. When considered alongside previously documented linear and triangular spatial relationships, the results suggest that curved proportional geometry may operate within an already structured coordinate network. The study’s primary contribution is methodological: it demonstrates that fixed-growth spiral models, when evaluated using bounded parameter grids and explicit Monte Carlo testing, provide a reproducible framework for assessing curved geometric hypotheses in complex landscapes.