Levy Flight Patterns in the Cortical Architecture of Macaca mulatta

Levy flights (LF), a concept originating in statistical physics, describe random walks in which the step lengths follow a heavy-tailed probability distribution, often a power law. Unlike Brownian motion, where step lengths are constrained within a narrow range, LF are characterized by the coexistence of many short steps interspersed with occasional long jumps. Applying advanced computational techniques, we looked for LF-like patterns in high-resolution histological images of Macaca mulatta (Rhesus macaque) cortical area 4 from BrainMaps.org. Step-length distributions, derived from pairwise distances between neuronal somata, exhibited heavy-tailed behavior consistent with power-law models across all samples. Maximum likelihood estimation of power-law exponents ( values: 0.87-1.08) strongly supported the heavy-tailed nature of these patterns, showing a better fit with power-law models compared to exponential or normal distributions. Connectivity analyses revealed a dual organizational structure within cortical layers: densely interconnected local clusters coexisting with sparse long-range connections. k-Nearest neighbors graphs demonstrated small-world network properties, with average clustering coefficients ranging from 0.622 to 0.630 across samples. This consistent structural organization aligns with LF principles, wherein local processing is optimized alongside global integration for efficiency and functionality. The implications extend to developmental biology, as the emergence of LF-like patterns likely reflects intrinsic self-organizing processes during embryonic and fetal development. This LF-like organization provides a natural framework for designing artificial networks that optimize performance in tasks requiring both localized specialization and global integration. Moreover, understanding the developmental origins of these patterns could guide strategies for neural repair and regeneration in stroke or neurodegenerative diseases.