Fractal analysis for 2D and 3D binary images

We present a unified, letter-coded framework for interpreting 2D and 3D binary images that groups descriptors into a complementary triad: global complexity, fragmentation/disorder, and connectivity. Applied to the Banat Mountains, we analyze three layers: tree cover (2000-2021), cumulative forest loss (2001-2021), and annual forest loss (2001-2021), using a parsimonious portfolio of fractal and non-fractal indices (box-counting and related dimensions, the fragmentation family FFI/FFDI/FTI, lacunarity, and succolarity) and their 3D analogues. The fragmentation family complements class-level FRAGSTATS metrics (e.g., edge density, clumpiness) by isolating scaling-sensitive edge irregularity and tentacularity. Results converge across dimensions: tree cover behaves as a compact, nearly space-filling matrix with high, stable connectivity, low disorder, declining lacunarity, and modest, non-systemwide gains in succolarity; annual loss shows episodic spikes in disorder and transient connectivity with reduced anisotropy. In 3D, tree cover is nearly space-filling, cumulative loss is intermediate and filamentary, and annual loss is sparse, with succolarity meaningful only for the matrix. We conclude with a practical monitoring set that captures the triad while minimizing redundancy and outline sensitivity and transferability to other mountainous, heterogeneous regions in Southeastern Europe.