Symmetrical Crystal Lattice Evolution

{ "prompt_type": "generative_crystal_simulation", "title": "Symmetrical Crystal Lattice Evolution", "summary": "Develop a WebGL-based 3D simulation of a crystal lattice that evolves via cellular automata rules, incorporating Voronoi tessellation for symmetric growth and diffusion-limited aggregation. Procedural audio generates harmonic resonances based on lattice vibrations; user interaction applies symmetry-breaking perturbations with elastic recovery.", "libraries": { "three_js": "https://t.co/6mVlOHh9Uu", "glsl_noise": "custom shader for Perlin noise", "tone_js": "https://t.co/Mul0ZcSBcw" }, "world": { "lattice": { "type": "cubic symmetric (FCC or BCC)", "size": [64, 64, 64], "symmetry_group": "O_h (octahedral symmetry with reflections)", "initial_state": "seed crystal at center with radial symmetry" }, "growth_model": { "cellular_automata": { "rules": "birth/survival based on neighbor count (e.g., 4-6 for growth)", "symmetry_enforcement": "mirror updates across 6 axes" }, "diffusion": "Fick's second law with anisotropy along crystal planes", "aggregation": "diffusion-limited (DLA) with probabilistic attachment" } }, "visual_rendering": { "geometry": { "voxels": "instanced meshes for efficiency", "symmetry_mapping": "quaternions for rotational symmetry", "fractal_detail": "subdivision levels 3-5 based on energy" }, "shaders": { "refraction": "Snell's law simulation for crystal facets", "iridescence": "thin-film interference with wavelength-dependent colors", "glow": "bloom post-processing with symmetric halos" } }, "audio": { "vibrations": { "modes": "normal modes from lattice phonons (Debye model)", "frequencies": "base 220 Hz, harmonics via golden ratio (1.618)", "amplitude": "proportional to growth rate" }, "generative": { "synth": "additive synthesis with symmetric waveforms (sine + cosine pairs)", "effects": "delay lines mirroring lattice symmetry" } }, "interactivity": { "perturbation": { "mouse_drag": "apply force vector, breaking symmetry temporarily", "recovery": "elastic spring model restores O_h group over 10 seconds" }, "view_modes": { "cross_section": "slice along symmetry planes", "time_lapse": "accelerate evolution x10" } }, "evolution_metrics": { "symmetry_index": "deviation from ideal O_h (measured via group theory metrics)", "energy": "Gibbs free energy simulation for stability", "complexity": "fractal dimension of boundary surfaces" }, "performance": { "lod": "reduce voxel resolution beyond 50 units", "multithreading": "workers for CA updates" }, "mathematical_models": { "group_theory": "symmetry operations for lattice transformations", "percolation_theory": "critical points for phase transitions", "harmonic_analysis": "Fourier transforms for vibration modes" }, "comments": [ "Octahedral symmetry ensures perfect geometric balance.", "Diffusion models create emergent fractal patterns.", "Audio harmonics reflect mathematical purity of lattice.", "Perturbations demonstrate resilience of symmetry." ] }