对称晶体晶格演化

{ "prompt_type": "生成式晶体模拟", "title": "对称晶格演化", "summary": "开发一个基于WebGL的3D晶格模拟，通过元胞自动机规则演化，结合Voronoi镶嵌实现对称生长和扩散限制聚集。程序化音频根据晶格振动生成和声共振；用户交互施加对称性破缺扰动，并具有弹性恢复。", "libraries": { "three_js": "https://t.co/6mVlOHh9Uu", "glsl_noise": "自定义着色器用于Perlin噪声", "tone_js": "https://t.co/Mul0ZcSBcw" }, "world": { "lattice": { "type": "立方对称（FCC或BCC）", "size": [64, 64, 64], "symmetry_group": "O_h（具有反射的八面体对称）", "initial_state": "中心种子晶体，具有径向对称" }, "growth_model": { "cellular_automata": { "rules": "基于邻居数量的出生/存活（例如，4-6用于生长）", "symmetry_enforcement": "沿6个轴镜像更新" }, "diffusion": "菲克第二定律，沿晶面各向异性", "aggregation": "扩散限制（DLA）与概率附着" } }, "visual_rendering": { "geometry": { "voxels": "实例化网格以提高效率", "symmetry_mapping": "四元数用于旋转对称", "fractal_detail": "基于能量的细分级别3-5" }, "shaders": { "refraction": "斯涅尔定律模拟晶体刻面", "iridescence": "薄膜干涉，波长相关颜色", "glow": "泛光后处理，对称光晕" } }, "audio": { "vibrations": { "modes": "来自晶格声子的简正模式（德拜模型）", "frequencies": "基频220 Hz，谐波通过黄金比例（1.618）", "amplitude": "与生长速率成正比" }, "generative": { "synth": "加性合成，对称波形（正弦+余弦对）", "effects": "延迟线镜像晶格对称" } }, "interactivity": { "perturbation": { "mouse_drag": "施加力向量，暂时打破对称", "recovery": "弹性弹簧模型在10秒内恢复O_h群" }, "view_modes": { "cross_section": "沿对称平面切片", "time_lapse": "加速演化x10" } }, "evolution_metrics": { "symmetry_index": "与理想O_h的偏差（通过群论度量）", "energy": "吉布斯自由能模拟稳定性", "complexity": "边界表面的分形维数" }, "performance": { "lod": "超过50单位时降低体素分辨率", "multithreading": "用于CA更新的工作线程" }, "mathematical_models": { "group_theory": "晶格变换的对称操作", "percolation_theory": "相变的临界点", "harmonic_analysis": "振动模式的傅里叶变换" }, "comments": [ "八面体对称确保完美的几何平衡。", "扩散模型产生涌现的分形图案。", "音频谐波反映晶格的数学纯度。", "扰动展示对称的弹性。" ] }