Leveraging Simplified Physics Models for Acceleration in Rendering

v3.1 supplement: Added a zip containing the Python scripts used for all lattice relaxations, plus selected visualization files showing the emergent primordial filament structure (strongest bonds only) in the relaxed lattice. Includes larger-N runs (up to 65,536) with slower cooling for longer strings, plus high-density stiff regions and low-density voids. DescriptionThis preprint presents a direct computational translation of the Entropic Universe Theory (EUT) pre-geometry into a practical rendering accelerator. The method applies the exact same normalized rigidity criterion r=∥∇S∥/Tr = \|\nabla S\| / Tr = \|\nabla S\| / T that selects stable d=3d = 3d = 3 in EUT II to prune low-importance regions in procedural scalar fields. On self-similar toy noise models the approach consistently prunes ≈66 % of computations across resolutions 512²–4096², delivering stable ≈3.0× performance and memory gains while perfectly preserving gradient-defined features. Realistic sparse content reaches ≈72 % savings. The work includes the first-ever rendered "mini EUT universe" (N=8,192 relaxed lattice at the β=3 attractor), proving that EUT’s predicted sparsity of structure applies directly to the emergent 3D pre-geometry itself. Full reproducibility is provided through a complete Colab notebook (included as supplementary material) that generates every figure and the mini-universe simulation. AbstractMemory bandwidth and compute constraints dominate modern GPU/CPU workloads in procedural rendering. Drawing directly from the final pre-geometry of the Entropic Universe Theory (EUT) - where emergent geometry and localized structure arise from gradients in a single scalar entropy density field - we propose a computational heuristic that mirrors EUT’s core emergence principle: rigidity r=∥∇S∥/Tr = \|\nabla S\| / Tr = \|\nabla S\| / T thresholds adaptive pruning of low-importance regions. In toy procedural noise models simulating self-similar scalar fields, the method consistently prunes ≈66 % of computations across resolutions (512²–4096²), yielding stable ≈3.0× gains while preserving gradient-defined features. This outcome is consistent with EUT’s predicted sparsity of structure in scalar fields with self-similar gradients. The approach is extremely cheap, unified, and CPU-friendly.