Geometric and Statistical Modeling of Large-Scale Spatial Similarity using Fibonacci-Based Metrics A Case Study of Terrestrial and Celestial Point Networks

Abstract

Comparing large spatial systems is difficult when the elements belong to different physical domains and scales. In this work, spatial similarity is examined using a combination of geometric ratios, angular relationships, and statistical testing, with particular emphasis on Fibonacci-based proportions. The analysis focuses on whether structured point networks exhibit measurable correspondence that exceeds random expectation. The terrestrial dataset consists of summit points and geomorphological reference locations in the Bosnian Valley of the Pyramids, derived from LiDAR surveys and geodetic measurements. The celestial dataset is based on high-precision astrometric coordinates of the main stars of the Pleiades cluster obtained from the Gaia mission. Distances between points were normalized and compared using golden-ratio thresholds, angular separations were evaluated within fixed tolerance limits, and overall geometric similarity was assessed through rotation- and scale-invariant Procrustes alignment. Several inter-point relationships on the terrestrial landscape approximate Fibonacci proportions within a 2% deviation. Angular relationships between corresponding point sets converge within ±2°, and Procrustes alignment produces a low root-mean-square deviation, indicating strong geometric similarity after normalization. To test whether such correspondence could arise by chance, 100,000 Monte Carlo simulations were performed using randomized point configurations constrained by the same spatial bounds. Only 2.1% of randomized cases produced equal or stronger similarity, yielding a p-value of 0.021. The results do not imply cultural intent or causal connection but demonstrate that the observed spatial coherence is statistically unlikely to be random under the applied constraints. The methods used here are reproducible and can be applied to other spatial modeling problems where proportional structure, orientation, and pattern similarity are of interest