Refracted Light Interaction in Turbulent Bubbling Water (RLITBW): A Macroscopic Fluid-Optic Entropy Source

Abstract

The demand for high quality, unpredictable random numbers is a fundamental requirement in cryptography, stochastic simulation, and optimization. While pseudo-random number generators (PRNGs) are computationally efficient, their deterministic nature limits their suitability for security-critical applications. True random number generators (TRNGs), although physically grounded, often rely on expensive quantum or tightly controlled electronic phenomena. This paper introduces a low-cost, macroscopic TRNG based on Refracted Light Interaction in Turbulent Bubbling Water (RLITBW). The proposed system exploits compound classical chaos arising from multiphase fluid dynamics and time-varying optical refraction. A physical-mathematical model is developed to describe the cascade of non-linear processes from stochastic bubble nucleation and turbulent ascent to chaotic optical path scrambling that collectively amplify microscopic uncertainties into measurable entropy.The raw optical signal is digitized and processed using a provably secure entropy-conditioning pipeline based on Toeplitz universal hashing, followed by deterministic cryptographic expansion. The chaotic nature of the physical source is empirically validated using phase-space reconstruction, Lyapunov exponent estimation, autocorrelation analysis, and entropy metrics. The conditioned output successfully passes the full NIST SP 800-22 statistical test suite and nonlinear dynamical measures including Lyapunov exponents and sample entropy. Beyond statistical validation, the generated randomness is applied to population-based optimization algorithms, demonstrating practical usability as a replacement for conventional PRNGs. Finally, deployment architectures and scalability considerations are discussed, positioning RLITBW as an accessible, reproducible, and economically viable entropy source for real-world systems.