Equation-Based Analog Video Storage and Display: A Unified Framework Using Modular Entropy and Pixel-Life Dynamics

<p dir="ltr"> We present a revolutionary approach to video storage and display that replaces traditional pixel-array representations with mathematical equation systems. By combining the modular entropy framework with pixel-life reaction-diffusion dynamics, we demonstrate that video content can be stored as compact equation parameters and reconstructed in real-time through analog field modulation. This approach achieves 30-50× compression ratios compared to modern codecs while providing resolution independence, continuous temporal evaluation, and energy reductions exceeding 90%. The system treats each pixel as a biochemical-like entity governed by stoichiometric reactions and standing wave patterns, creating "living" displays where content emerges from mathematical computation rather than static memory. We provide complete mathematical formulations, hardware specifications, encoding/decoding algorithms, and demonstrate applications ranging from infinite-zoom displays to adaptive medical imaging systems. Experimental validation shows storage requirements of <30 MB for 10 minutes of 4K video with lossless reconstruction at arbitrary resolutions and frame rates</p>