Ice-wedge polygon centres are more ordered than a random tessellation: structure-factor analysis of a million-polygon network with heterogeneity-limited long-range order

Ice-wedge polygons tile vast areas of permafrost lowland and are a textbook example of a self-organised fracture pattern with a characteristic length. How ordered that pattern is — in the precise sense used for disordered hyperuniform media — has not been quantified. Using a lidar-derived inventory of 1.16 million ice-wedge polygons south of Prudhoe Bay, Alaska (Abolt & Young, 2019/2020), we treat the polygon centres as a planar point pattern and compute the pair correlation g(r), the structure factor S(k) and the number variance, comparing against complete spatial randomness, an inhomogeneous-Poisson null matched to the local density, and — crucially — a Poisson–Voronoi tessellation (the centroids of a random tessellation of the same density). Polygon centres show hard-core exclusion and a characteristic spacing of ~15 m, and a deep structure-factor suppression, S_min ≈ 0.1, at intermediate wavenumber. This suppression is genuine: it lies far below the inhomogeneous-Poisson null in every window analysed, and below the Poisson–Voronoi null in the most uniform windows — so the ice-wedge crack network is more ordered than a random space-filling tessellation. Long-range hyperuniformity is, however, not confirmed: S(k→0) remains finite and the number variance grows faster than the window area (σ² ∝ R^2.7), because real geomorphic heterogeneity — spatial variation in polygon size and coverage — dominates the largest scales; the suppression deepens in more uniform windows, indicating a heterogeneity-limited rather than intrinsic floor. Comparing intact (low-centred) and thermokarst-degraded (high-centred) terrain matched for uniformity, the intermediate-range order persists through degradation: thermokarst inverts the microtopographic relief but preserves the planimetric network order. Ice-wedge polygon centres are thus a locally rigid, intermediate-range-ordered disordered pattern with a hyperuniform tendency that is masked at long range by landscape heterogeneity. All analysis code and derived per-window statistics are openly available; the raw inventory is from Abolt & Young (PANGAEA, CC-BY-4.0).