Traditional cryptographic hash functions rely on structured, deterministic transformations, which may limit their adaptability and unpredictability. In this work, we investigate a chaos-based hashing mechanism that leverages the nonlinear and highly sensitive dynamics of a double pendulum. By simulating the double pendulum and solving its equations of motion, we analyze the influence of various input parameters and initial conditions on the resulting hash outputs. The inherent unpredictability of the system introduces a high degree of entropy and diffusion, key properties for effective cryptographic hashing. To evaluate the robustness and effectiveness of our approach, we compare its performance against widely used hash functions such as MD5 and SHA-256, using statistical metrics including Hamming distance and bit uniformity. The resulting hash function, ChaoticHash3, achieved a higher average Hamming distance (128.089 vs. 127.998 for SHA-256), a more uniform bit distribution as shown by a higher chi-square p-value (~0.03), and slightly higher Shannon entropy (3.45022 vs. 3.43204 for SHA-256), supporting the viability of chaotic systems for generating secure and unpredictable hash outputs.