nanocode/particle-lab/09-lorenz/index.html

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    <title>09 - LORENZ | 洛伦兹吸引子</title>
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    <div class="info">
        <h1>09 - LORENZ</h1>
        <p>洛伦兹吸引子 - 蝴蝶效应</p>
        <p>σ=10, ρ=28, β=8/3</p>
        <p>粒子数: <span id="count">0</span></p>
        <p>FPS: <span id="fps">0</span></p>
    </div>
    <div class="formula">
        <div>微分方程组:</div>
        <code>dx/dt = σ(y - x)</code>
        <code>dy/dt = x(ρ - z) - y</code>
        <code>dz/dt = xy - βz</code>
    </div>

    <script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>
    <script src="https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/controls/OrbitControls.js"></script>
    <script src="https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/postprocessing/EffectComposer.js"></script>
    <script src="https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/postprocessing/RenderPass.js"></script>
    <script src="https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/postprocessing/ShaderPass.js"></script>
    <script src="https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/shaders/CopyShader.js"></script>
    <script src="https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/shaders/LuminosityHighPassShader.js"></script>
    <script src="https://cdn.jsdelivr.net/npm/three@0.128.0/examples/js/postprocessing/UnrealBloomPass.js"></script>

    <script>
        const COUNT = 6000;
        const sigma = 10, rho = 28, beta = 8/3;
        
        const scene = new THREE.Scene();
        scene.fog = new THREE.FogExp2(0x000000, 0.003);
        const camera = new THREE.PerspectiveCamera(60, window.innerWidth / window.innerHeight, 0.1, 2000);
        camera.position.set(60, 40, 60);
        
        const renderer = new THREE.WebGLRenderer({ antialias: true, powerPreference: "high-performance" });
        renderer.setSize(window.innerWidth, window.innerHeight);
        renderer.setPixelRatio(Math.min(window.devicePixelRatio, 2));
        document.getElementById('canvas-container').appendChild(renderer.domElement);

        const controls = new THREE.OrbitControls(camera, renderer.domElement);
        controls.enableDamping = true;
        controls.autoRotate = true;
        controls.autoRotateSpeed = 0.3;

        const renderScene = new THREE.RenderPass(scene, camera);
        const bloomPass = new THREE.UnrealBloomPass(new THREE.Vector2(window.innerWidth, window.innerHeight), 1.5, 0.4, 0);
        bloomPass.strength = 2.0; bloomPass.radius = 0.6; bloomPass.threshold = 0;
        const composer = new THREE.EffectComposer(renderer);
        composer.addPass(renderScene);
        composer.addPass(bloomPass);

        const dummy = new THREE.Object3D();
        const color = new THREE.Color();
        const geometry = new THREE.SphereGeometry(0.25, 8, 8);
        const material = new THREE.MeshBasicMaterial({ color: 0xffffff });
        const instancedMesh = new THREE.InstancedMesh(geometry, material, COUNT);
        instancedMesh.instanceMatrix.setUsage(THREE.DynamicDrawUsage);
        scene.add(instancedMesh);

        // 洛伦兹轨迹点
        const trajectories = [];
        const trailLength = 50;
        
        for (let i = 0; i < COUNT; i++) {
            trajectories.push({
                x: (Math.random() - 0.5) * 20,
                y: (Math.random() - 0.5) * 20 + 20,
                z: (Math.random() - 0.5) * 20 + 25,
                trail: [],
                phase: i / COUNT * Math.PI * 2
            });
        }

        document.getElementById('count').textContent = COUNT;
        let lastTime = performance.now(), frameCount = 0;
        const fpsEl = document.getElementById('fps');
        const clock = new THREE.Clock();

        function lorenzStep(x, y, z, dt) {
            const dx = sigma * (y - x) * dt;
            const dy = (x * (rho - z) - y) * dt;
            const dz = (x * y - beta * z) * dt;
            return { x: x + dx, y: y + dy, z: z + dz };
        }

        function animate() {
            requestAnimationFrame(animate);
            const now = performance.now();
            frameCount++;
            if (now - lastTime >= 1000) { fpsEl.textContent = frameCount; frameCount = 0; lastTime = now; }

            const time = clock.getElapsedTime();
            const dt = 0.008;

            for (let i = 0; i < COUNT; i++) {
                const t = trajectories[i];
                
                // 洛伦兹迭代
                const next = lorenzStep(t.x, t.y, t.z, dt);
                t.x = next.x; t.y = next.y; t.z = next.z;
                
                // 添加扰动防止全部收敛
                if (Math.random() < 0.001) {
                    t.x += (Math.random() - 0.5) * 2;
                    t.y += (Math.random() - 0.5) * 2;
                }
                
                // 更新轨迹
                t.trail.push({x: t.x, y: t.y, z: t.z});
                if (t.trail.length > trailLength) t.trail.shift();
                
                // 在轨迹上显示（制造拖尾效果）
                const trailPos = t.trail[Math.floor((Math.sin(time * 2 + t.phase) + 1) / 2 * (t.trail.length - 1))] || t.trail[0];
                
                dummy.position.set(trailPos.x, trailPos.y, trailPos.z);
                dummy.scale.setScalar(0.8 + Math.sin(time * 3 + i * 0.01) * 0.3);
                dummy.updateMatrix();
                instancedMesh.setMatrixAt(i, dummy.matrix);
                
                // 颜色：基于速度和位置
                const speed = Math.sqrt(Math.pow(next.x - t.x, 2) + Math.pow(next.y - t.y, 2)) / dt;
                const hue = 0.95 + (t.y - 20) / 40 * 0.1; // 粉红到紫色
                const lightness = 0.4 + Math.min(speed / 50, 0.4);
                color.setHSL(hue, 0.9, lightness);
                instancedMesh.setColorAt(i, color);
            }

            instancedMesh.instanceMatrix.needsUpdate = true;
            instancedMesh.instanceColor.needsUpdate = true;
            controls.update();
            composer.render();
        }
        animate();

        window.addEventListener('resize', () => {
            camera.aspect = window.innerWidth / window.innerHeight;
            camera.updateProjectionMatrix();
            renderer.setSize(window.innerWidth, window.innerHeight);
            composer.setSize(window.innerWidth, window.innerHeight);
        });
    </script>
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