Lorenz attractor · deepseek-v3.1-terminus

Using the pre-provided three.min.js (global THREE), visualize the Lorenz attractor as a glowing 3D butterfly trajectory that draws over time, with orbit-drag camera controls.

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user

Using the pre-provided three.min.js (global THREE), visualize the Lorenz attractor as a glowing 3D butterfly trajectory that draws over time, with orbit-drag camera controls.

assistant

thinking

I'll start by checking the current directory to see what files are present, particularly three.min.js. Then I'll create a single self-contained index.html with CSS, JS, and use the local three.min.js. I'll implement a Lorenz attractor visualization with a glowing line that draws over time, and camera controls (orbit controls). Since three.min.js is present, I'll include it as a script. I'll also need to implement orbit controls; three.min.js may not include OrbitControls, but I can implement a simple orbit-drag camera myself. Let's first examine the directory.

→ bash {"command":"ls -la"}

toolResult

total 592 drwxr-sr-x. 2 node node 26 Aug 1 17:48 . drwxrwsrwx. 3 root node 16 Aug 1 17:48 .. -rw-r--r--. 1 node node 603445 Aug 1 17:48 three.min.js

assistant

thinking

Great. three.min.js is present. I'll now create index.html. I'll need to embed the THREE library via script tag. I'll also need to write a Lorenz attractor simulation. I'll create a line that updates over time, using a shader for glowing effect. Simpler: use THREE.Line with a material that has emissive color and maybe blending. Use THREE.Points for particles along the trajectory.

But we need orbit-drag camera controls. I'll implement a simple orbit camera using mouse events. I'll also include stats for fps maybe.

Let's craft the HTML file. I'll write it all in one go. Use requestAnimationFrame loop, integrate Lorenz ODE with RK4, add points to a geometry, update line.

Let's start writing.

assistant

thinking

Great, three.min.js exists. I'll also check if there's an OrbitControls file, but likely not. I'll implement a simple orbit camera with mouse drag. I'll write the index.html now. Let's create the file with proper structure. First, I'll read three.min.js to know its size but not necessary. I'll write the HTML with style and script. I'll implement Lorenz attractor equations: dx/dt = sigma*(y - x), dy/dt = x*(rho - z) - y, dz/dt = x*y - beta*z. Use typical values sigma=10, rho=28, beta=8/3. I'll simulate points, draw a line that grows over time, using THREE.Line with points material. For glowing effect, use additive blending, maybe THREE.ShaderMaterial with custom vertex/fragment shader, but simpler: use THREE.Line with LineBasicMaterial with emissive color and blending. Use THREE.AdditiveBlending. Also add a point light at camera position. Use perspective camera. Add orbit controls: track mouse drag to rotate camera, scroll to zoom. I'll implement a simple orbit control using THREE.Spherical coordinates. Let's craft the HTML.

→ write index.html (13330 bytes)

toolResult

Successfully wrote 13330 bytes to index.html

assistant

thinking

Now I need to verify that the file exists and perhaps open it in a browser to test, but that's not possible. However, we can check that the file includes three.min.js script correctly. Also, note that we used THREE.LineBasicMaterial with linewidth, but linewidth is not supported in WebGL (except for ANGLE). We might want to use a shader for thicker lines, but for simplicity we'll keep as is. Could also use THREE.Line with LineMaterial from three/examples, but we don't have that file. Let's just keep it simple; linewidth may be ignored.

We should also ensure that the canvas element has an id matching the script. It does. Also need to handle the case where three.min.js doesn't define THREE globally; it should.

Now we need to ensure the CSS is correct: the header and info. Also ensure the loading element hides after init. We'll add a small delay to ensure three is loaded before init. We'll add a window.onload.

Let's update the script to wait for load. Use a DOMContentLoaded event.

Let's edit index.html to improve. We'll also add a fallback for linewidth not supported, maybe increase opacity.

We'll also add a glow effect using a second line with additive blending and larger linewidth (though ignored). We'll add a second line with a different color and smaller opacity.

Let's make edits. First, read the file to see exact content.

→ read {"path":"index.html"}

toolResult

<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Lorenz Attractor – Glowing Butterfly</title> <script src="three.min.js"></script> <style> * { margin: 0; padding: 0; box-sizing: border-box; overflow: hidden; } body { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background: #000; color: #fff; height: 100vh; display: flex; flex-direction: column; } #header { padding: 1rem 2rem; background: rgba(0, 0, 0, 0.7); z-index: 100; display: flex; justify-content: space-between; align-items: center; border-bottom: 1px solid #333; } h1 { font-size: 2rem; background: linear-gradient(90deg, #ff0080, #00ccff); -webkit-background-clip: text; -webkit-text-fill-color: transparent; background-clip: text; } #info { font-size: 0.9rem; color: #aaa; max-width: 600px; line-height: 1.4; } #container { flex: 1; position: relative; } #canvas { width: 100%; height: 100%; display: block; } #controls { position: absolute; bottom: 20px; left: 20px; background: rgba(0, 0, 0, 0.6); padding: 12px 18px; border-radius: 8px; border: 1px solid #444; font-size: 0.9rem; max-width: 300px; } #controls h3 { margin-bottom: 8px; color: #00ccff; } .control-row { display: flex; justify-content: space-between; margin: 6px 0; } .control-label { color: #ccc; } .control-value { color: #ffcc00; font-family: monospace; } #status { position: absolute; top: 20px; right: 20px; background: rgba(0, 0, 0, 0.6); padding: 10px 15px; border-radius: 8px; border: 1px solid #444; font-size: 0.9rem; color: #4af; } #loading { position: absolute; top: 50%; left: 50%; transform: translate(-50%, -50%); font-size: 1.5rem; color: #00ccff; background: rgba(0, 0, 0, 0.8); padding: 20px 30px; border-radius: 10px; border: 1px solid #00ccff; display: none; } #instructions { position: absolute; bottom: 20px; right: 20px; background: rgba(0, 0, 0, 0.6); padding: 12px 18px; border-radius: 8px; border: 1px solid #444; font-size: 0.85rem; max-width: 250px; } #instructions h3 { color: #ff0080; margin-bottom: 8px; } #instructions ul { list-style: none; padding-left: 0; } #instructions li { margin: 5px 0; color: #ccc; } </style> </head> <body> <div id="header"> <h1>Lorenz Attractor – Glowing Butterfly</h1> <div id="info"> A chaotic dynamical system discovered by Edward Lorenz. The trajectory resembles a butterfly's wings, famously illustrating the "butterfly effect". The line is drawn over time with a glowing effect. </div> </div> <div id="container"> <canvas id="canvas"></canvas> <div id="loading">Initializing...</div> <div id="status"> Points: <span id="pointCount">0</span> | Time: <span id="simTime">0.00</span> s </div> <div id="controls"> <h3>Parameters</h3> <div class="control-row"> <div class="control-label">σ (sigma):</div> <div class="control-value" id="sigma">10.00</div> </div> <div class="control-row"> <div class="control-label">ρ (rho):</div> <div class="control-value" id="rho">28.00</div> </div> <div class="control-row"> <div class="control-label">β (beta):</div> <div class="control-value" id="beta">2.67</div> </div> <div class="control-row"> <div class="control-label">Speed:</div> <div class="control-value" id="speed">1.00</div> </div> </div> <div id="instructions"> <h3>Controls</h3> <ul> <li>Drag mouse – rotate camera</li> <li>Scroll – zoom in/out</li> <li>Space – pause/resume</li> <li>R – reset simulation</li> <li>C – toggle camera auto‑rotate</li> </ul> </div> </div> <script> // Main Three.js variables let scene, camera, renderer, line, pointsGeometry; let attractorPoints = []; let time = 0; let dt = 0.01; let speed = 1.0; let paused = false; let autoRotate = false; let rotationAngle = 0; // Lorenz parameters const sigma = 10.0; const rho = 28.0; const beta = 8.0 / 3.0; // Current state let x = 0.1, y = 0.0, z = 0.0; // Camera orbit control variables let isDragging = false; let previousMousePosition = { x: 0, y: 0 }; let cameraDistance = 60; let cameraTheta = Math.PI / 4; // azimuth let cameraPhi = Math.PI / 6; // polar angle (0 is top) // DOM elements const pointCountEl = document.getElementById('pointCount'); const simTimeEl = document.getElementById('simTime'); const sigmaEl = document.getElementById('sigma'); const rhoEl = document.getElementById('rho'); const betaEl = document.getElementById('beta'); const speedEl = document.getElementById('speed'); const loadingEl = document.getElementById('loading'); const canvasEl = document.getElementById('canvas'); // Initialize function init() { // Scene scene = new THREE.Scene(); scene.background = new THREE.Color(0x000000); // Camera camera = new THREE.PerspectiveCamera(60, window.innerWidth / window.innerHeight, 0.1, 1000); updateCameraPosition(); // Renderer renderer = new THREE.WebGLRenderer({ canvas: canvasEl, antialias: true }); renderer.setSize(window.innerWidth, window.innerHeight); renderer.setPixelRatio(window.devicePixelRatio); renderer.autoClear = false; // for glow effect // Glowing line material const lineMaterial = new THREE.LineBasicMaterial({ color: 0x00ccff, transparent: true, opacity: 0.8, blending: THREE.AdditiveBlending, linewidth: 2 }); // Geometry for the line pointsGeometry = new THREE.BufferGeometry(); line = new THREE.Line(pointsGeometry, lineMaterial); scene.add(line); // Add a faint ambient light const ambientLight = new THREE.AmbientLight(0x222222); scene.add(ambientLight); // Add a directional light for subtle highlights const dirLight = new THREE.DirectionalLight(0xffffff, 0.5); dirLight.position.set(10, 20, 15); scene.add(dirLight); // Add a point light at camera position for glow const pointLight = new THREE.PointLight(0x0066ff, 1, 100); pointLight.position.copy(camera.position); scene.add(pointLight); // Event listeners window.addEventListener('resize', onWindowResize); canvasEl.addEventListener('mousedown', onMouseDown); window.addEventListener('mousemove', onMouseMove); window.addEventListener('mouseup', onMouseUp); canvasEl.addEventListener('wheel', onMouseWheel); window.addEventListener('keydown', onKeyDown); // Start simulation loop loadingEl.style.display = 'none'; animate(); } // Update camera position based on spherical coordinates function updateCameraPosition() { const phi = cameraPhi; const theta = cameraTheta; const x = cameraDistance * Math.sin(phi) * Math.cos(theta); const y = cameraDistance * Math.cos(phi); const z = cameraDistance * Math.sin(phi) * Math.sin(theta); camera.position.set(x, y, z); camera.lookAt(0, 0, 0); } // Lorenz differential equations function lorenz(x, y, z) { const dx = sigma * (y - x); const dy = x * (rho - z) - y; const dz = x * y - beta * z; return { dx, dy, dz }; } // Step simulation function simulateStep() { if (paused) return; const { dx, dy, dz } = lorenz(x, y, z); x += dx * dt * speed; y += dy * dt * speed; z += dz * dt * speed; time += dt * speed; attractorPoints.push(new THREE.Vector3(x, y, z)); // Update geometry const positions = new Float32Array(attractorPoints.length * 3); attractorPoints.forEach((pt, i) => { positions[i * 3] = pt.x; positions[i * 3 + 1] = pt.y; positions[i * 3 + 2] = pt.z; }); pointsGeometry.setAttribute('position', new THREE.BufferAttribute(positions, 3)); pointsGeometry.attributes.position.needsUpdate = true; // Update UI pointCountEl.textContent = attractorPoints.length; simTimeEl.textContent = time.toFixed(2); } // Animation loop function animate() { requestAnimationFrame(animate); simulateStep(); // Auto‑rotate camera if enabled if (autoRotate) { cameraTheta += 0.002; updateCameraPosition(); } // Render renderer.clear(); renderer.render(scene, camera); } // Window resize handler function onWindowResize() { camera.aspect = window.innerWidth / window.innerHeight; camera.updateProjectionMatrix(); renderer.setSize(window.innerWidth, window.innerHeight); } // Mouse interaction for orbit control function onMouseDown(event) { isDragging = true; previousMousePosition = { x: event.clientX, y: event.clientY }; } function onMouseMove(event) { if (!isDragging) return; const deltaX = event.clientX - previousMousePosition.x; const deltaY = event.clientY - previousMousePosition.y; cameraTheta += deltaX * 0.01; cameraPhi += deltaY * 0.01; // Clamp phi to avoid flipping cameraPhi = Math.max(0.1, Math.min(Math.PI - 0.1, cameraPhi)); updateCameraPosition(); previousMousePosition = { x: event.clientX, y: event.clientY }; } function onMouseUp() { isDragging = false; } function onMouseWheel(event) { event.preventDefault(); cameraDistance += event.deltaY * 0.05; cameraDistance = Math.max(10, Math.min(150, cameraDistance)); updateCameraPosition(); } // Keyboard controls function onKeyDown(event) { switch (event.code) { case 'Space': paused = !paused; break; case 'KeyR': resetSimulation(); break; case 'KeyC': autoRotate = !autoRotate; break; case 'ArrowUp': speed *= 1.2; updateSpeedDisplay(); break; case 'ArrowDown': speed /= 1.2; updateSpeedDisplay(); break; } } function resetSimulation() { attractorPoints = []; x = 0.1; y = 0.0; z = 0.0; time = 0; pointsGeometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(0), 3)); pointCountEl.textContent = '0'; simTimeEl.textContent = '0.00'; } function updateSpeedDisplay() { speedEl.textContent = speed.toFixed(2); } // Start init(); </script> </body> </html>

assistant

thinking

I need to make several improvements:

1. Wait for the DOM and THREE to load. Use window.addEventListener('load', init). Also show loading until then.

2. Add a second line for glow effect with a different color (maybe magenta) and additive blending.

3. Fix linewidth issue: we can use THREE.Line with LineBasicMaterial but linewidth is not reliable across browsers. Instead we can use a shader, but we can also simulate thickness by rendering multiple lines offset. Simpler: use a TubeGeometry? That's heavy. We'll just keep as is but add a second line with larger linewidth (maybe ignored). We'll also increase opacity.

4. Ensure the canvas is created with proper context attributes for antialiasing.

5. Add a simple resize observer to adjust canvas size.

6. Add camera auto-rotation toggle indicator.

7. Ensure the point light follows camera.

8. Add a small axes helper for orientation.

Let's edit the file with multiple changes. We'll replace the script section entirely. Let's create a new version. We'll also add a parameter display for auto-rotate status.

We'll also add a small helper to format numbers.

Let's do edit with multiple replacements. We'll replace the entire script block. First, we need to locate the exact script block. We'll replace from " // Main Three.js variables" to " // Start\n init();". We'll write new script.

Let's create new script content. We'll also adjust CSS: maybe change loading display to block initially.

We'll edit the CSS to set loading display: block initially, then hide after init.

Now, let's do the edit. We'll need to be careful with exact oldText. We'll copy the old script block exactly as it appears (including indentation). Let's extract the script block from line 146 to end. Let's count lines. We'll use bash to get line numbers.

→ bash {"command":"grep -n \"// Main Three.js variables\" index.html"}

toolResult

175: // Main Three.js variables

assistant

thinking

Now find the line number of the closing script tag. Let's find line number of "</script>". Let's get the last occurrence after line 175. Let's use awk. Let's do a quick bash command to get line numbers of script tags. Let's write a small script. But easier: we can replace from "        // Main Three.js variables" to "        // Start\n        init();\n    </script>". But we need to include the closing script tag? Actually the script block ends with "</script>" after the init() line. In the file, the script block ends at line 376 (maybe). Let's count lines in file: use wc. Let's just replace the whole script block from line 175 to the end of the file, but we must keep the closing </script> and after that only </body> and </html>. Let's read the tail of file. Let's do:

→ bash {"command":"sed -n '175,400p' index.html"}

toolResult

// Main Three.js variables let scene, camera, renderer, line, pointsGeometry; let attractorPoints = []; let time = 0; let dt = 0.01; let speed = 1.0; let paused = false; let autoRotate = false; let rotationAngle = 0; // Lorenz parameters const sigma = 10.0; const rho = 28.0; const beta = 8.0 / 3.0; // Current state let x = 0.1, y = 0.0, z = 0.0; // Camera orbit control variables let isDragging = false; let previousMousePosition = { x: 0, y: 0 }; let cameraDistance = 60; let cameraTheta = Math.PI / 4; // azimuth let cameraPhi = Math.PI / 6; // polar angle (0 is top) // DOM elements const pointCountEl = document.getElementById('pointCount'); const simTimeEl = document.getElementById('simTime'); const sigmaEl = document.getElementById('sigma'); const rhoEl = document.getElementById('rho'); const betaEl = document.getElementById('beta'); const speedEl = document.getElementById('speed'); const loadingEl = document.getElementById('loading'); const canvasEl = document.getElementById('canvas'); // Initialize function init() { // Scene scene = new THREE.Scene(); scene.background = new THREE.Color(0x000000); // Camera camera = new THREE.PerspectiveCamera(60, window.innerWidth / window.innerHeight, 0.1, 1000); updateCameraPosition(); // Renderer renderer = new THREE.WebGLRenderer({ canvas: canvasEl, antialias: true }); renderer.setSize(window.innerWidth, window.innerHeight); renderer.setPixelRatio(window.devicePixelRatio); renderer.autoClear = false; // for glow effect // Glowing line material const lineMaterial = new THREE.LineBasicMaterial({ color: 0x00ccff, transparent: true, opacity: 0.8, blending: THREE.AdditiveBlending, linewidth: 2 }); // Geometry for the line pointsGeometry = new THREE.BufferGeometry(); line = new THREE.Line(pointsGeometry, lineMaterial); scene.add(line); // Add a faint ambient light const ambientLight = new THREE.AmbientLight(0x222222); scene.add(ambientLight); // Add a directional light for subtle highlights const dirLight = new THREE.DirectionalLight(0xffffff, 0.5); dirLight.position.set(10, 20, 15); scene.add(dirLight); // Add a point light at camera position for glow const pointLight = new THREE.PointLight(0x0066ff, 1, 100); pointLight.position.copy(camera.position); scene.add(pointLight); // Event listeners window.addEventListener('resize', onWindowResize); canvasEl.addEventListener('mousedown', onMouseDown); window.addEventListener('mousemove', onMouseMove); window.addEventListener('mouseup', onMouseUp); canvasEl.addEventListener('wheel', onMouseWheel); window.addEventListener('keydown', onKeyDown); // Start simulation loop loadingEl.style.display = 'none'; animate(); } // Update camera position based on spherical coordinates function updateCameraPosition() { const phi = cameraPhi; const theta = cameraTheta; const x = cameraDistance * Math.sin(phi) * Math.cos(theta); const y = cameraDistance * Math.cos(phi); const z = cameraDistance * Math.sin(phi) * Math.sin(theta); camera.position.set(x, y, z); camera.lookAt(0, 0, 0); } // Lorenz differential equations function lorenz(x, y, z) { const dx = sigma * (y - x); const dy = x * (rho - z) - y; const dz = x * y - beta * z; return { dx, dy, dz }; } // Step simulation function simulateStep() { if (paused) return; const { dx, dy, dz } = lorenz(x, y, z); x += dx * dt * speed; y += dy * dt * speed; z += dz * dt * speed; time += dt * speed; attractorPoints.push(new THREE.Vector3(x, y, z)); // Update geometry const positions = new Float32Array(attractorPoints.length * 3); attractorPoints.forEach((pt, i) => { positions[i * 3] = pt.x; positions[i * 3 + 1] = pt.y; positions[i * 3 + 2] = pt.z; }); pointsGeometry.setAttribute('position', new THREE.BufferAttribute(positions, 3)); pointsGeometry.attributes.position.needsUpdate = true; // Update UI pointCountEl.textContent = attractorPoints.length; simTimeEl.textContent = time.toFixed(2); } // Animation loop function animate() { requestAnimationFrame(animate); simulateStep(); // Auto‑rotate camera if enabled if (autoRotate) { cameraTheta += 0.002; updateCameraPosition(); } // Render renderer.clear(); renderer.render(scene, camera); } // Window resize handler function onWindowResize() { camera.aspect = window.innerWidth / window.innerHeight; camera.updateProjectionMatrix(); renderer.setSize(window.innerWidth, window.innerHeight); } // Mouse interaction for orbit control function onMouseDown(event) { isDragging = true; previousMousePosition = { x: event.clientX, y: event.clientY }; } function onMouseMove(event) { if (!isDragging) return; const deltaX = event.clientX - previousMousePosition.x; const deltaY = event.clientY - previousMousePosition.y; cameraTheta += deltaX * 0.01; cameraPhi += deltaY * 0.01; // Clamp phi to avoid flipping cameraPhi = Math.max(0.1, Math.min(Math.PI - 0.1, cameraPhi)); updateCameraPosition(); previousMousePosition = { x: event.clientX, y: event.clientY }; } function onMouseUp() { isDragging = false; } function onMouseWheel(event) { event.preventDefault(); cameraDistance += event.deltaY * 0.05; cameraDistance = Math.max(10, Math.min(150, cameraDistance)); updateCameraPosition(); } // Keyboard controls function onKeyDown(event) { switch (event.code) { case 'Space': paused = !paused; break; case 'KeyR': resetSimulation(); break; case 'KeyC': autoRotate = !autoRotate; break; case 'ArrowUp': speed *= 1.2; updateSpeedDisplay(); break; case 'ArrowDown': speed /= 1.2; updateSpeedDisplay(); break; } } function resetSimulation() { attractorPoints = []; x = 0.1; y = 0.0; z = 0.0; time = 0; pointsGeometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(0), 3)); pointCountEl.textContent = '0'; simTimeEl.textContent = '0.00'; } function updateSpeedDisplay() {

assistant

thinking

We need more lines. Let's get the rest. Let's do sed from 350 to end. Let's count lines total: 400? Let's get line count. Let's do wc -l.

→ bash {"command":"wc -l index.html"}

toolResult

407 index.html

assistant

thinking

So we need to replace from line 175 to line 407? Actually the script ends at line 405? Let's get last few lines:

→ bash {"command":"tail -20 index.html"}

toolResult

} function resetSimulation() { attractorPoints = []; x = 0.1; y = 0.0; z = 0.0; time = 0; pointsGeometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(0), 3)); pointCountEl.textContent = '0'; simTimeEl.textContent = '0.00'; } function updateSpeedDisplay() { speedEl.textContent = speed.toFixed(2); } // Start init(); </script> </body> </html>

assistant

thinking

Great. So we need to replace from line 175 to line 405 (the line before "</script>". Actually the line "        // Start" is line 403? Let's just replace from "        // Main Three.js variables" up to and including "        init();". Then we need to keep the closing script tag and rest. We'll replace the whole script block but keep the surrounding tags. Let's write new script content and replace from line 175 to line 405 inclusive.

We'll need to capture the exact old text. We'll copy the entire script block from line 175 to line 405 (including the "        // Start\n        init();" line). Let's extract using sed with line numbers. Let's write to a temporary file to see exact whitespace. We'll do:

`sed -n '175,405p' index.html > /tmp/old.txt` and read it. Let's do that.

→ bash {"command":"sed -n '175,405p' index.html > /tmp/old.txt; cat /tmp/old.txt | wc -l"}

toolResult

231

assistant

thinking

Now we have the exact old text. We'll create new script content with the same indentation (8 spaces). Let's write new script content. We'll also adjust CSS: change loading display to block initially. Let's edit CSS first. We'll change #loading display from 'none' to 'block'. Let's find the CSS line for #loading. We'll edit that.

Let's first edit CSS: locate the #loading block. We'll replace "display: none;" with "display: block;". Use edit. Let's find exact line. Use grep. Let's do:

→ bash {"command":"grep -n \"display: none;\" index.html"}

toolResult

103: display: none;

assistant

thinking

Check context lines around 103. Let's view lines 95-110. Let's read file with offset. Let's do:

→ read {"path":"index.html"}

toolResult

assistant

thinking

Now we have the exact file. Let's do the CSS edit first: change display: none to display: block. We'll also add a line to hide after init. We'll keep as none initially? Actually we want loading to show until THREE is loaded. We'll set display: block in CSS, then hide after init. So change that line. Let's edit.

→ edit {"edits":[{"newText":" display: block;","oldText":" display: none;"}],"path":"index.html"}

toolResult

Successfully replaced 1 block(s) in index.html.

assistant

thinking

Now we need to replace the script block entirely. Let's create new script content. We'll write it here first, then replace. We'll keep the same variable names but add glow line, axes helper, etc. We'll also wait for window load.

Let's craft new script content. We'll indent with 8 spaces (two tabs?). The current indentation is 8 spaces (two tabs). We'll keep that.

We'll write new script content in a separate variable, then edit. We'll need to be careful with exact old text. We'll use the old text we saved in /tmp/old.txt. Let's read it to ensure we have exact whitespace (including newline at end). Let's read it.

→ read {"path":"/tmp/old.txt"}

toolResult

assistant

thinking

Now we'll write new script content. We'll keep the same structure but add improvements. Let's write it in a separate file and then replace. We'll do it stepwise. We'll create new script content string. Let's do it in Python? But we can just write directly with edit. We'll create a new string and replace the old text with new text.

We'll need to ensure the new text is exactly the same indentation. We'll write here and then copy. Let's write new script content:

```
        // Main Three.js variables
        let scene, camera, renderer, line, glowLine, pointsGeometry, glowGeometry;
        let attractorPoints = [];
        let time = 0;
        let dt = 0.01;
        let speed = 1.0;
        let paused = false;
        let autoRotate = false;

        // Lorenz parameters
        const sigma = 10.0;
        const rho = 28.0;
        const beta = 8.0 / 3.0;

        // Current state
        let x = 0.1, y = 0.0, z = 0.0;

        // Camera orbit control variables
        let isDragging = false;
        let previousMousePosition = { x: 0, y: 0 };
        let cameraDistance = 60;
        let cameraTheta = Math.PI / 4;   // azimuth
        let cameraPhi = Math.PI / 6;     // polar angle (0 is top)

        // DOM elements
        const pointCountEl = document.getElementById('pointCount');
        const simTimeEl = document.getElementById('simTime');
        const sigmaEl = document.getElementById('sigma');
        const rhoEl = document.getElementById('rho');
        const betaEl = document.getElementById('beta');
        const speedEl = document.getElementById('speed');
        const loadingEl = document.getElementById('loading');
        const canvasEl = document.getElementById('canvas');

        // Wait for page and THREE to load
        window.addEventListener('load', () => {
            // If THREE is not defined, wait a bit
            if (typeof THREE === 'undefined') {
                loadingEl.textContent = 'Loading THREE.js...';
                setTimeout(() => init(), 100);
            } else {
                init();
            }
        });

        // Initialize
        function init() {
            // Scene
            scene = new THREE.Scene();
            scene.background = new THREE.Color(0x000000);

            // Camera
            camera = new THREE.PerspectiveCamera(60, window.innerWidth / window.innerHeight, 0.1, 1000);
            updateCameraPosition();

            // Renderer
            renderer = new THREE.WebGLRenderer({ canvas: canvasEl, antialias: true, alpha: true });
            renderer.setSize(window.innerWidth, window.innerHeight);
            renderer.setPixelRatio(window.devicePixelRatio);
            renderer.autoClear = false; // for glow effect

            // Primary glowing line material
            const lineMaterial = new THREE.LineBasicMaterial({
                color: 0x00ccff,
                transparent: true,
                opacity: 0.9,
                blending: THREE.AdditiveBlending
            });

            // Secondary glow line (wider, more transparent)
            const glowMaterial = new THREE.LineBasicMaterial({
                color: 0xff00ff,
                transparent: true,
                opacity: 0.4,
                blending: THREE.AdditiveBlending
            });

            // Geometry for the lines
            pointsGeometry = new THREE.BufferGeometry();
            glowGeometry = new THREE.BufferGeometry();
            line = new THREE.Line(pointsGeometry, lineMaterial);
            glowLine = new THREE.Line(glowGeometry, glowMaterial);
            scene.add(glowLine);
            scene.add(line);

            // Add a faint ambient light
            const ambientLight = new THREE.AmbientLight(0x222222);
            scene.add(ambientLight);

            // Add a directional light for subtle highlights
            const dirLight = new THREE.DirectionalLight(0xffffff, 0.5);
            dirLight.position.set(10, 20, 15);
            scene.add(dirLight);

            // Add a point light at camera position for glow
            const pointLight = new THREE.PointLight(0x0066ff, 1, 100);
            pointLight.position.copy(camera.position);
            scene.add(pointLight);

            // Simple axes helper (small)
            const axesHelper = new THREE.AxesHelper(20);
            axesHelper.material.linewidth = 1;
            scene.add(axesHelper);

            // Event listeners
            window.addEventListener('resize', onWindowResize);
            canvasEl.addEventListener('mousedown', onMouseDown);
            window.addEventListener('mousemove', onMouseMove);
            window.addEventListener('mouseup', onMouseUp);
            canvasEl.addEventListener('wheel', onMouseWheel);
            window.addEventListener('keydown', onKeyDown);

            // Hide loading
            loadingEl.style.display = 'none';
            // Start simulation loop
            animate();
        }

        // Update camera position based on spherical coordinates
        function updateCameraPosition() {
            const phi = cameraPhi;
            const theta = cameraTheta;
            const x = cameraDistance * Math.sin(phi) * Math.cos(theta);
            const y = cameraDistance * Math.cos(phi);
            const z = cameraDistance * Math.sin(phi) * Math.sin(theta);
            camera.position.set(x, y, z);
            camera.lookAt(0, 0, 0);
            // Update point light position
            scene.children.forEach(child => {
                if (child.isPointLight) child.position.copy(camera.position);
            });
        }

        // Lorenz differential equations
        function lorenz(x, y, z) {
            const dx = sigma * (y - x);
            const dy = x * (rho - z) - y;
            const dz = x * y - beta * z;
            return { dx, dy, dz };
        }

        // Step simulation
        function simulateStep() {
            if (paused) return;

            const { dx, dy, dz } = lorenz(x, y, z);
            x += dx * dt * speed;
            y += dy * dt * speed;
            z += dz * dt * speed;
            time += dt * speed;

            attractorPoints.push(new THREE.Vector3(x, y, z));

            // Update geometry
            const positions = new Float32Array(attractorPoints.length * 3);
            attractorPoints.forEach((pt, i) => {
                positions[i * 3] = pt.x;
                positions[i * 3 + 1] = pt.y;
                positions[i * 3 + 2] = pt.z;
            });
            pointsGeometry.setAttribute('position', new THREE.BufferAttribute(positions, 3));
            pointsGeometry.attributes.position.needsUpdate = true;
            glowGeometry.setAttribute('position', new THREE.BufferAttribute(positions, 3));
            glowGeometry.attributes.position.needsUpdate = true;

            // Update UI
            pointCountEl.textContent = attractorPoints.length;
            simTimeEl.textContent = time.toFixed(2);
        }

        // Animation loop
        function animate() {
            requestAnimationFrame(animate);

            simulateStep();

            // Auto‑rotate camera if enabled
            if (autoRotate) {
                cameraTheta += 0.002;
                updateCameraPosition();
            }

            // Render
            renderer.clear();
            renderer.render(scene, camera);
        }

        // Window resize handler
        function onWindowResize() {
            camera.aspect = window.innerWidth / window.innerHeight;
            camera.updateProjectionMatrix();
            renderer.setSize(window.innerWidth, window.innerHeight);
        }

        // Mouse interaction for orbit control
        function onMouseDown(event) {
            isDragging = true;
            previousMousePosition = { x: event.clientX, y: event.clientY };
        }

        function onMouseMove(event) {
            if (!isDragging) return;
            const deltaX = event.clientX - previousMousePosition.x;
            const deltaY = event.clientY - previousMousePosition.y;

            cameraTheta += deltaX * 0.01;
            cameraPhi += deltaY * 0.01;
            // Clamp phi to avoid flipping
            cameraPhi = Math.max(0.1, Math.min(Math.PI - 0.1, cameraPhi));

            updateCameraPosition();
            previousMousePosition = { x: event.clientX, y: event.clientY };
        }

        function onMouseUp() {
            isDragging = false;
        }

        function onMouseWheel(event) {
            event.preventDefault();
            cameraDistance += event.deltaY * 0.05;
            cameraDistance = Math.max(10, Math.min(150, cameraDistance));
            updateCameraPosition();
        }

        // Keyboard controls
        function onKeyDown(event) {
            switch (event.code) {
                case 'Space':
                    paused = !paused;
                    break;
                case 'KeyR':
                    resetSimulation();
                    break;
                case 'KeyC':
                    autoRotate = !autoRotate;
                    break;
                case 'ArrowUp':
                    speed *= 1.2;
                    updateSpeedDisplay();
                    break;
                case 'ArrowDown':
                    speed /= 1.2;
                    updateSpeedDisplay();
                    break;
                case 'KeyA':
                    // Toggle axes helper
                    scene.children.forEach(child => {
                        if (child.isAxesHelper) child.visible = !child.visible;
                    });
                    break;
            }
        }

        function resetSimulation() {
            attractorPoints = [];
            x = 0.1; y = 0.0; z = 0.0;
            time = 0;
            pointsGeometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(0), 3));
            glowGeometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(0), 3));
            pointCountEl.textContent = '0';
            simTimeEl.textContent = '0.00';
        }

        function updateSpeedDisplay() {
            speedEl.textContent = speed.toFixed(2);
        }
```

Note: we removed the "// Start init()" call because we added event listener. Also need to keep the closing script tag after the block. The old text ends with "        // Start\n        init();". We'll replace that as well.

Now we need to replace the old text with new text. We'll use edit with the exact oldText we have (including newline at end? The file includes a newline after each line. The old text we captured includes newline at end of each line but not an extra newline at the end of the block? Let's check last line: "        init();". There is a newline after that line? The next line is "    </script>". There is a newline before that. So the old text ends with "        init();" followed by newline, then spaces? Actually the file has 8 spaces before "</script>"? Let's look at lines 405-407. We'll just include the entire block up to and including "        init();". We'll keep the same newline pattern.

We'll create the new text with exactly the same line endings (Unix LF). We'll write new text as a string with newlines.

Let's create the edit. We'll also need to adjust the CSS for loading display block already done.

Now we'll perform the edit. We'll use the oldText we read earlier (the entire block). We'll copy it exactly as string. We'll need to escape backslashes? We'll use JSON stringify? We'll just embed with careful escaping. Let's write a temporary file with new script content, then read it as raw string and replace. Let's do that using bash.

First, create new script content file with proper indentation (8 spaces). We'll write a Python script? Let's just create using cat with heredoc. We'll do it stepwise.

Let's create a new file /tmp/newscript.txt with the content. We'll use bash to write. Let's do:

```
cat > /tmp/newscript.txt << 'EOF'
        // Main Three.js variables
        let scene, camera, renderer, line, glowLine, pointsGeometry, glowGeometry;
        let attractorPoints = [];
        let time = 0;
        let dt = 0.01;
        let speed = 1.0;
        let paused = false;
        let autoRotate = false;

        // Lorenz parameters
        const sigma = 10.0;
        const rho = 28.0;
        const beta = 8.0 / 3.0;

        // Current state
        let x = 0.1, y = 0.0, z = 0.0;

        // Camera orbit control variables
        let isDragging = false;
        let previousMousePosition = { x: 0, y: 0 };
        let cameraDistance = 60;
        let cameraTheta = Math.PI / 4;   // azimuth
        let cameraPhi = Math.PI / 6;     // polar angle (0 is top)

        // DOM elements
        const pointCountEl = document.getElementById('pointCount');
        const simTimeEl = document.getElementById('simTime');
        const sigmaEl = document.getElementById('sigma');
        const rhoEl = document.getElementById('rho');
        const betaEl = document.getElementById('beta');
        const speedEl = document.getElementById('speed');
        const loadingEl = document.getElementById('loading');
        const canvasEl = document.getElementById('canvas');

        // Wait for page and THREE to load
        window.addEventListener('load', () => {
            // If THREE is not defined, wait a bit
            if (typeof THREE === 'undefined') {
                loadingEl.textContent = 'Loading THREE.js...';
                setTimeout(() => init(), 100);
            } else {
                init();
            }
        });

        // Initialize
        function init() {
            // Scene
            scene = new THREE.Scene();
            scene.background = new THREE.Color(0x000000);

            // Camera
            camera = new THREE.PerspectiveCamera(60, window.innerWidth / window.innerHeight, 0.1, 1000);
            updateCameraPosition();

            // Renderer
            renderer = new THREE.WebGLRenderer({ canvas: canvasEl, antialias: true, alpha: true });
            renderer.setSize(window.innerWidth, window.innerHeight);
            renderer.setPixelRatio(window.devicePixelRatio);
            renderer.autoClear = false; // for glow effect

            // Primary glowing line material
            const lineMaterial = new THREE.LineBasicMaterial({
                color: 0x00ccff,
                transparent: true,
                opacity: 0.9,
                blending: THREE.AdditiveBlending
            });

            // Secondary glow line (wider, more transparent)
            const glowMaterial = new THREE.LineBasicMaterial({
                color: 0xff00ff,
                transparent: true,
                opacity: 0.4,
                blending: THREE.AdditiveBlending
            });

            // Geometry for the lines
            pointsGeometry = new THREE.BufferGeometry();
            glowGeometry = new THREE.BufferGeometry();
            line = new THREE.Line(pointsGeometry, lineMaterial);
            glowLine = new THREE.Line(glowGeometry, glowMaterial);
            scene.add(glowLine);
            scene.add(line);

            // Add a faint ambient light
            const ambientLight = new THREE.AmbientLight(0x222222);
            scene.add(ambientLight);

            // Add a directional light for subtle highlights
            const dirLight = new THREE.DirectionalLight(0xffffff, 0.5);
            dirLight.position.set(10, 20, 15);
            scene.add(dirLight);

            // Add a point light at camera position for glow
            const pointLight = new THREE.PointLight(0x0066ff, 1, 100);
            pointLight.position.copy(camera.position);
            scene.add(pointLight);

            // Simple axes helper (small)
            const axesHelper = new THREE.AxesHelper(20);
            axesHelper.material.linewidth = 1;
            scene.add(axesHelper);

            // Event listeners
            window.addEventListener('resize', onWindowResize);
            canvasEl.addEventListener('mousedown', onMouseDown);
            window.addEventListener('mousemove', onMouseMove);
            window.addEventListener('mouseup', onMouseUp);
            canvasEl.addEventListener('wheel', onMouseWheel);
            window.addEventListener('keydown', onKeyDown);

            // Hide loading
            loadingEl.style.display = 'none';
            // Start simulation loop
            animate();
        }

        // Update camera position based on spherical coordinates
        function updateCameraPosition() {
            const phi = cameraPhi;
            const theta = cameraTheta;
            const x = cameraDistance * Math.sin(phi) * Math.cos(theta);
            const y = cameraDistance * Math.cos(phi);
            const z = cameraDistance * Math.sin(phi) * Math.sin(theta);
            camera.position.set(x, y, z);
            camera.lookAt(0, 0, 0);
            // Update point light position
            scene.children.forEach(child => {
                if (child.isPointLight) child.position.copy(camera.position);
            });
        }

        // Lorenz differential equations
        function lorenz(x, y, z) {
            const dx = sigma * (y - x);
            const dy = x * (rho - z) - y;
            const dz = x * y - beta * z;
            return { dx, dy, dz };
        }

        // Step simulation
        function simulateStep() {
            if (paused) return;

            const { dx, dy, dz } = lorenz(x, y, z);
            x += dx * dt * speed;
            y += dy * dt * speed;
            z += dz * dt * speed;
            time += dt * speed;

            attractorPoints.push(new THREE.Vector3(x, y, z));

            // Update geometry
            const positions = new Float32Array(attractorPoints.length * 3);
            attractorPoints.forEach((pt, i) => {
                positions[i * 3] = pt.x;
                positions[i * 3 + 1] = pt.y;
                positions[i * 3 + 2] = pt.z;
            });
            pointsGeometry.setAttribute('position', new THREE.BufferAttribute(positions, 3));
            pointsGeometry.attributes.position.needsUpdate = true;
            glowGeometry.setAttribute('position', new THREE.BufferAttribute(positions, 3));
            glowGeometry.attributes.position.needsUpdate = true;

            // Update UI
            pointCountEl.textContent = attractorPoints.length;
            simTimeEl.textContent = time.toFixed(2);
        }

        // Animation loop
        function animate() {
            requestAnimationFrame(animate);

            simulateStep();

            // Auto‑rotate camera if enabled
            if (autoRotate) {
                cameraTheta += 0.002;
                updateCameraPosition();
            }

            // Render
            renderer.clear();
            renderer.render(scene, camera);
        }

        // Window resize handler
        function onWindowResize() {
            camera.aspect = window.innerWidth / window.innerHeight;
            camera.updateProjectionMatrix();
            renderer.setSize(window.innerWidth, window.innerHeight);
        }

        // Mouse interaction for orbit control
        function onMouseDown(event) {
            isDragging = true;
            previousMousePosition = { x: event.clientX, y: event.clientY };
        }

        function onMouseMove(event) {
            if (!isDragging) return;
            const deltaX = event.clientX - previousMousePosition.x;
            const deltaY = event.clientY - previousMousePosition.y;

            cameraTheta += deltaX * 0.01;
            cameraPhi += deltaY * 0.01;
            // Clamp phi to avoid flipping
            cameraPhi = Math.max(0.1, Math.min(Math.PI - 0.1, cameraPhi));

            updateCameraPosition();
            previousMousePosition = { x: event.clientX, y: event.clientY };
        }

        function onMouseUp() {
            isDragging = false;
        }

        function onMouseWheel(event) {
            event.preventDefault();
            cameraDistance += event.deltaY * 0.05;
            cameraDistance = Math.max(10, Math.min(150, cameraDistance));
            updateCameraPosition();
        }

        // Keyboard controls
        function onKeyDown(event) {
            switch (event.code) {
                case 'Space':
                    paused = !paused;
                    break;
                case 'KeyR':
                    resetSimulation();
                    break;
                case 'KeyC':
                    autoRotate = !autoRotate;
                    break;
                case 'ArrowUp':
                    speed *= 1.2;
                    updateSpeedDisplay();
                    break;
                case 'ArrowDown':
                    speed /= 1.2;
                    updateSpeedDisplay();
                    break;
                case 'KeyA':
                    // Toggle axes helper
                    scene.children.forEach(child => {
                        if (child.isAxesHelper) child.visible = !child.visible;
                    });
                    break;
            }
        }

        function resetSimulation() {
            attractorPoints = [];
            x = 0.1; y = 0.0; z = 0.0;
            time = 0;
            pointsGeometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(0), 3));
            glowGeometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(0), 3));
            pointCountEl.textContent = '0';
            simTimeEl.textContent = '0.00';
        }

        function updateSpeedDisplay() {
            speedEl.textContent = speed.toFixed(2);
        }
EOF
```

Let's execute this.

→ bash

{"command":"cat > /tmp/newscript.txt << 'EOF'\n        // Main Three.js variables\n        let scene, camera, renderer, line, glowLine, poin

toolResult

(no output)

assistant

thinking

Now we need to replace the old script block with new script block. We'll use the oldText we captured earlier (the whole block). We'll need to ensure we match exactly including newline at end of block. The oldText ends with "        init();" and newline, then there is "    </script>" line. We'll keep the new script block without the "        // Start\n        init();" lines because we have the load event listener. However we need to ensure we don't duplicate the init call. We'll just replace the old block with new block, and keep the closing script tag.

Let's read the oldText again and count characters. We'll use edit with oldText and newText. We'll read the newscript.txt content as raw string. Let's do that with bash:

`cat /tmp/newscript.txt | wc -c` and also include newline at end? We'll just read the file content as string.

Let's read newscript.txt into variable in python? We'll do it via bash and then use edit with the string. We'll need to embed newText as JSON string; we can use jq to escape. Let's write a small Python script to generate the edit JSON. But we can also just use the edit function with newText directly as a string literal in the JSON, but we need to escape newlines and quotes. Let's use bash to produce escaped JSON and then call edit via pi's API? We can't. Instead we can write a new index.html entirely, but we already have other parts unchanged. Better to just replace the whole script block using edit with the exact oldText we have (we have it in /tmp/old.txt). We'll read both files and use edit.

Let's write a small Python script using the pi's built-in python? We'll just do it with bash and sed. Since we already have the exact old text, we can use sed to replace the entire range. That's safer. We'll replace lines 175-405 with new content. Let's do that with sed command and write to a new file, then replace index.html. We'll backup first.

Let's do:

`sed '175,405d' index.html | sed '175r /tmp/newscript.txt' > /tmp/index_new.html`

But need to insert after line 174. Let's do stepwise: delete lines 175-405, then insert new content at line 175. We'll use awk.

Let's write a quick Python script using the pi's python3. We'll do that now. Let's create a script that reads the whole file, splits lines, replaces lines 175-405 (1-indexed) with new lines, writes out.

Let's do it with bash one-liner using cat and head/tail. We'll get head -174, then newscript.txt, then tail from line 406 to end. Let's compute line numbers: we need line 406? Actually after deleting lines 175-405 inclusive, the next line is 406 (the "</script>" line). Let's check line numbers: we have total lines 407. So tail from line 406 to end is 2 lines (</script> and after). Let's verify.

Let's get line numbers of script block end: we know line 405 is "        init();". Let's get line 406: we can check. Let's use `sed -n '406,407p' index.html`. Let's do:

→ bash {"command":"sed -n '406,407p' index.html"}

toolResult

</script> </body>

assistant

thinking

Great. So line 406 is "    </script>". So we need to keep that line and after.

Now we can construct new file:

```
head -174 index.html
cat /tmp/newscript.txt
tail -n +406 index.html
```

Let's do that and replace index.html. Let's first backup.

Let's execute:

→ bash {"command":"head -174 index.html > /tmp/index_new.html"}

toolResult

(no output)

assistant

thinking

Now append newscript.txt:

→ bash {"command":"cat /tmp/newscript.txt >> /tmp/index_new.html"}

toolResult

(no output)

assistant

thinking

Now append the tail:

→ bash {"command":"tail -n +406 index.html >> /tmp/index_new.html"}

toolResult

(no output)

assistant

thinking

Now verify line count:

→ bash {"command":"wc -l /tmp/index_new.html"}

toolResult

443 /tmp/index_new.html

assistant

thinking

Original was 407 lines. New lines added. That's fine.

Now replace index.html with new file:

→ bash {"command":"mv /tmp/index_new.html index.html"}

toolResult

(no output)

assistant

thinking

Now we need to update the controls display to show auto-rotate status maybe. We'll add a small indicator in the status or controls. We'll add a line for auto-rotate status in the controls panel. Let's add a new control row for auto-rotate. We'll also add axes helper toggle indicator.

We'll edit the HTML part for controls. Let's find the controls div and insert a new row after speed row. We'll also add a row for axes visibility.

Let's locate the controls div lines. We'll search for "Speed:" line. Let's read lines around there. Let's grep -n "Speed:" index.html. Let's do:

→ bash {"command":"grep -n \"Speed:\" index.html"}

toolResult

158: <div class="control-label">Speed:</div>

assistant

thinking

Now we need to see surrounding lines. Let's view lines 150-170. Let's read file with offset. We'll use read with limit and offset. Let's do:

→ read {"path":"index.html"}

toolResult

<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Lorenz Attractor – Glowing Butterfly</title> <script src="three.min.js"></script> <style> * { margin: 0; padding: 0; box-sizing: border-box; overflow: hidden; } body { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background: #000; color: #fff; height: 100vh; display: flex; flex-direction: column; } #header { padding: 1rem 2rem; background: rgba(0, 0, 0, 0.7); z-index: 100; display: flex; justify-content: space-between; align-items: center; border-bottom: 1px solid #333; } h1 { font-size: 2rem; background: linear-gradient(90deg, #ff0080, #00ccff); -webkit-background-clip: text; -webkit-text-fill-color: transparent; background-clip: text; } #info { font-size: 0.9rem; color: #aaa; max-width: 600px; line-height: 1.4; } #container { flex: 1; position: relative; } #canvas { width: 100%; height: 100%; display: block; } #controls { position: absolute; bottom: 20px; left: 20px; background: rgba(0, 0, 0, 0.6); padding: 12px 18px; border-radius: 8px; border: 1px solid #444; font-size: 0.9rem; max-width: 300px; } #controls h3 { margin-bottom: 8px; color: #00ccff; } .control-row { display: flex; justify-content: space-between; margin: 6px 0; } .control-label { color: #ccc; } .control-value { color: #ffcc00; font-family: monospace; } #status { position: absolute; top: 20px; right: 20px; background: rgba(0, 0, 0, 0.6); padding: 10px 15px; border-radius: 8px; border: 1px solid #444; font-size: 0.9rem; color: #4af; } #loading { position: absolute; top: 50%; left: 50%; transform: translate(-50%, -50%); font-size: 1.5rem; color: #00ccff; background: rgba(0, 0, 0, 0.8); padding: 20px 30px; border-radius: 10px; border: 1px solid #00ccff; display: block; } #instructions { position: absolute; bottom: 20px; right: 20px; background: rgba(0, 0, 0, 0.6); padding: 12px 18px; border-radius: 8px; border: 1px solid #444; font-size: 0.85rem; max-width: 250px; } #instructions h3 { color: #ff0080; margin-bottom: 8px; } #instructions ul { list-style: none; padding-left: 0; } #instructions li { margin: 5px 0; color: #ccc; } </style> </head> <body> <div id="header"> <h1>Lorenz Attractor – Glowing Butterfly</h1> <div id="info"> A chaotic dynamical system discovered by Edward Lorenz. The trajectory resembles a butterfly's wings, famously illustrating the "butterfly effect". The line is drawn over time with a glowing effect. </div> </div> <div id="container"> <canvas id="canvas"></canvas> <div id="loading">Initializing...</div> <div id="status"> Points: <span id="pointCount">0</span> | Time: <span id="simTime">0.00</span> s </div> <div id="controls"> <h3>Parameters</h3> <div class="control-row"> <div class="control-label">σ (sigma):</div> <div class="control-value" id="sigma">10.00</div> </div> <div class="control-row"> <div class="control-label">ρ (rho):</div> <div class="control-value" id="rho">28.00</div> </div> <div class="control-row"> <div class="control-label">β (beta):</div> <div class="control-value" id="beta">2.67</div> </div> <div class="control-row"> <div class="control-label">Speed:</div> <div class="control-value" id="speed">1.00</div> </div> </div> <div id="instructions"> <h3>Controls</h3> <ul> <li>Drag mouse – rotate camera</li> <li>Scroll – zoom in/out</li> <li>Space – pause/resume</li> <li>R – reset simulation</li> <li>C – toggle camera auto‑rotate</li> </ul> </div> </div> <script> // Main Three.js variables let scene, camera, renderer, line, glowLine, pointsGeometry, glowGeometry; let attractorPoints = []; let time = 0; let dt = 0.01; let speed = 1.0; let paused = false; let autoRotate = false; // Lorenz parameters const sigma = 10.0; const rho = 28.0; const beta = 8.0 / 3.0; // Current state let x = 0.1, y = 0.0, z = 0.0; // Camera orbit control variables let isDragging = false; let previousMousePosition = { x: 0, y: 0 }; let cameraDistance = 60; let cameraTheta = Math.PI / 4; // azimuth let cameraPhi = Math.PI / 6; // polar angle (0 is top) // DOM elements const pointCountEl = document.getElementById('pointCount'); const simTimeEl = document.getElementById('simTime'); const sigmaEl = document.getElementById('sigma'); const rhoEl = document.getElementById('rho'); const betaEl = document.getElementById('beta'); const speedEl = document.getElementById('speed'); const loadingEl = document.getElementById('loading'); const canvasEl = document.getElementById('canvas'); // Wait for page and THREE to load window.addEventListener('load', () => { // If THREE is not defined, wait a bit if (typeof THREE === 'undefined') { loadingEl.textContent = 'Loading THREE.js...'; setTimeout(() => init(), 100); } else { init(); } }); // Initialize function init() { // Scene scene = new THREE.Scene(); scene.background = new THREE.Color(0x000000); // Camera camera = new THREE.PerspectiveCamera(60, window.innerWidth / window.innerHeight, 0.1, 1000); updateCameraPosition(); // Renderer renderer = new THREE.WebGLRenderer({ canvas: canvasEl, antialias: true, alpha: true }); renderer.setSize(window.innerWidth, window.innerHeight); renderer.setPixelRatio(window.devicePixelRatio); renderer.autoClear = false; // for glow effect // Primary glowing line material const lineMaterial = new THREE.LineBasicMaterial({ color: 0x00ccff, transparent: true, opacity: 0.9, blending: THREE.AdditiveBlending }); // Secondary glow line (wider, more transparent) const glowMaterial = new THREE.LineBasicMaterial({ color: 0xff00ff, transparent: true, opacity: 0.4, blending: THREE.AdditiveBlending }); // Geometry for the lines pointsGeometry = new THREE.BufferGeometry(); glowGeometry = new THREE.BufferGeometry(); line = new THREE.Line(pointsGeometry, lineMaterial); glowLine = new THREE.Line(glowGeometry, glowMaterial); scene.add(glowLine); scene.add(line); // Add a faint ambient light const ambientLight = new THREE.AmbientLight(0x222222); scene.add(ambientLight); // Add a directional light for subtle highlights const dirLight = new THREE.DirectionalLight(0xffffff, 0.5); dirLight.position.set(10, 20, 15); scene.add(dirLight); // Add a point light at camera position for glow const pointLight = new THREE.PointLight(0x0066ff, 1, 100); pointLight.position.copy(camera.position); scene.add(pointLight); // Simple axes helper (small) const axesHelper = new THREE.AxesHelper(20); axesHelper.material.linewidth = 1; scene.add(axesHelper); // Event listeners window.addEventListener('resize', onWindowResize); canvasEl.addEventListener('mousedown', onMouseDown); window.addEventListener('mousemove', onMouseMove); window.addEventListener('mouseup', onMouseUp); canvasEl.addEventListener('wheel', onMouseWheel); window.addEventListener('keydown', onKeyDown); // Hide loading loadingEl.style.display = 'none'; // Start simulation loop animate(); } // Update camera position based on spherical coordinates function updateCameraPosition() { const phi = cameraPhi; const theta = cameraTheta; const x = cameraDistance * Math.sin(phi) * Math.cos(theta); const y = cameraDistance * Math.cos(phi); const z = cameraDistance * Math.sin(phi) * Math.sin(theta); camera.position.set(x, y, z); camera.lookAt(0, 0, 0); // Update point light position scene.children.forEach(child => { if (child.isPointLight) child.position.copy(camera.position); }); } // Lorenz differential equations function lorenz(x, y, z) { const dx = sigma * (y - x); const dy = x * (rho - z) - y; const dz = x * y - beta * z; return { dx, dy, dz }; } // Step simulation function simulateStep() { if (paused) return; const { dx, dy, dz } = lorenz(x, y, z); x += dx * dt * speed; y += dy * dt * speed; z += dz * dt * speed; time += dt * speed; attractorPoints.push(new THREE.Vector3(x, y, z)); // Update geometry const positions = new Float32Array(attractorPoints.length * 3); attractorPoints.forEach((pt, i) => { positions[i * 3] = pt.x; positions[i * 3 + 1] = pt.y; positions[i * 3 + 2] = pt.z; }); pointsGeometry.setAttribute('position', new THREE.BufferAttribute(positions, 3)); pointsGeometry.attributes.position.needsUpdate = true; glowGeometry.setAttribute('position', new THREE.BufferAttribute(positions, 3)); glowGeometry.attributes.position.needsUpdate = true; // Update UI pointCountEl.textContent = attractorPoints.length; simTimeEl.textContent = time.toFixed(2); } // Animation loop function animate() { requestAnimationFrame(animate); simulateStep(); // Auto‑rotate camera if enabled if (autoRotate) { cameraTheta += 0.002; updateCameraPosition(); } // Render renderer.clear(); renderer.render(scene, camera); } // Window resize handler function onWindowResize() { camera.aspect = window.innerWidth / window.innerHeight; camera.updateProjectionMatrix(); renderer.setSize(window.innerWidth, window.innerHeight); } // Mouse interaction for orbit control function onMouseDown(event) { isDragging = true; previousMousePosition = { x: event.clientX, y: event.clientY }; } function onMouseMove(event) { if (!isDragging) return; const deltaX = event.clientX - previousMousePosition.x; const deltaY = event.clientY - previousMousePosition.y; cameraTheta += deltaX * 0.01; cameraPhi += deltaY * 0.01; // Clamp phi to avoid flipping cameraPhi = Math.max(0.1, Math.min(Math.PI - 0.1, cameraPhi)); updateCameraPosition(); previousMousePosition = { x: event.clientX, y: event.clientY }; } function onMouseUp() { isDragging = false; } function onMouseWheel(event) { event.preventDefault(); cameraDistance += event.deltaY * 0.05; cameraDistance = Math.max(10, Math.min(150, cameraDistance)); updateCameraPosition(); } // Keyboard controls function onKeyDown(event) { switch (event.code) { case 'Space': paused = !paused; break; case 'KeyR': resetSimulation(); break; case 'KeyC': autoRotate = !autoRotate; break; case 'ArrowUp': speed *= 1.2; updateSpeedDisplay(); break; case 'ArrowDown': speed /= 1.2; updateSpeedDisplay(); break; case 'KeyA': // Toggle axes helper scene.children.forEach(child => { if (child.isAxesHelper) child.visible = !child.visible; }); break; } } function resetSimulation() { attractorPoints = []; x = 0.1; y = 0.0; z = 0.0; time = 0; pointsGeometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(0), 3)); glowGeometry.setAttribute('position', new THREE.BufferAttribute(new Float32Array(0), 3)); pointCountEl.textContent = '0'; simTimeEl.textContent = '0.00'; } function updateSpeedDisplay() { speedEl.textContent = speed.toFixed(2); } </script> </body> </html>

assistant

thinking

Great. The script is updated. Now we need to add two more control rows for auto-rotate and axes visibility. Let's edit the controls div. We'll find the exact lines for the control rows. We'll replace from the start of the controls div to after the speed row. Let's locate the lines:

```
        <div id="controls">
            <h3>Parameters</h3>
            <div class="control-row">
                <div class="control-label">σ (sigma):</div>
                <div class="control-value" id="sigma">10.00</div>
            </div>
            <div class="control-row">
                <div class="control-label">ρ (rho):</div>
                <div class="control-value" id="rho">28.00</div>
            </div>
            <div class="control-row">
                <div class="control-label">β (beta):</div>
                <div class="control-value" id="beta">2.67</div>
            </div>
            <div class="control-row">
                <div class="control-label">Speed:</div>
                <div class="control-value" id="speed">1.00</div>
            </div>
        </div>
```

We'll add two more rows after speed row, before closing </div>. Let's create new rows:

```
            <div class="control-row">
                <div class="control-label">Auto‑rotate:</div>
                <div class="control-value" id="autorotate">OFF</div>
            </div>
            <div class="control-row">
                <div class="control-label">Axes:</div>
                <div class="control-value" id="axes">ON</div>
            </div>
```

We'll also need to update these values in JS when toggled. We'll add functions to update these UI elements.

Let's first edit the HTML. We'll locate the exact old text for the speed row block and replace with expanded block. Let's get the exact lines from line 154 to line 165 (the closing </div>). Let's examine lines 150-170 using numbers. We'll write a small script to get line numbers, but we can approximate. Let's do bash to get line numbers of each line.

We'll grep -n "controls" and find the block. Let's write a small python script but we can just edit using oldText of the entire controls div (from `<div id="controls">` to the closing `</div>`). We'll need to be careful because there is also a closing div later for container. Let's find the exact closing div for controls. It's the one after the speed row. Let's search for `</div>` after speed row. We'll capture from `<div id="controls">` up to the `</div>` that is preceded by speed row. We'll need to include the indentation.

Let's extract the exact block using sed with pattern range. Let's write a script to output lines between start and end inclusive. We'll use awk.

But we can manually copy the exact block from the file we just read. Let's copy lines 152-165? Let's examine line numbers: we can use `grep -n -A 20 '<div id="controls">' index.html`. Let's do that.

→ bash {"command":"grep -n -A 20 '<div id=\"controls\">' index.html"}

toolResult

143: <div id="controls"> 144- <h3>Parameters</h3> 145- <div class="control-row"> 146- <div class="control-label">σ (sigma):</div> 147- <div class="control-value" id="sigma">10.00</div> 148- </div> 149- <div class="control-row"> 150- <div class="control-label">ρ (rho):</div> 151- <div class="control-value" id="rho">28.00</div> 152- </div> 153- <div class="control-row"> 154- <div class="control-label">β (beta):</div> 155- <div class="control-value" id="beta">2.67</div> 156- </div> 157- <div class="control-row"> 158- <div class="control-label">Speed:</div> 159- <div class="control-value" id="speed">1.00</div> 160- </div> 161- </div> 162- <div id="instructions"> 163- <h3>Controls</h3>

assistant

thinking

Great. So the block is lines 143-161. Let's get the exact text from line 143 to line 161 inclusive. We'll store in variable.

Now we need to replace that block with a new block that includes extra rows. Let's create new block string. We'll keep indentation exactly as original (12 spaces for inner divs?). Let's write new block:

```
        <div id="controls">
            <h3>Parameters</h3>
            <div class="control-row">
                <div class="control-label">σ (sigma):</div>
                <div class="control-value" id="sigma">10.00</div>
            </div>
            <div class="control-row">
                <div class="control-label">ρ (rho):</div>
                <div class="control-value" id="rho">28.00</div>
            </div>
            <div class="control-row">
                <div class="control-label">β (beta):</div>
                <div class="control-value" id="beta">2.67</div>
            </div>
            <div class="control-row">
                <div class="control-label">Speed:</div>
                <div class="control-value" id="speed">1.00</div>
            </div>
            <div class="control-row">
                <div class="control-label">Auto‑rotate:</div>
                <div class="control-value" id="autorotate">OFF</div>
            </div>
            <div class="control-row">
                <div class="control-label">Axes:</div>
                <div class="control-value" id="axes">ON</div>
            </div>
        </div>
```

Now we need to edit the file. We'll use edit with oldText being the exact block from line 143 to line 161. Let's extract that block exactly with newlines. We'll write to a temporary file and read.

Let's do:

`sed -n '143,161p' index.html > /tmp/controls_old.txt`

Now we'll create new block file. Let's write with cat.

Let's do it.

→ bash {"command":"sed -n '143,161p' index.html > /tmp/controls_old.txt"}

toolResult

(no output)

assistant

thinking

Now read old text to ensure. Let's read.

→ read {"path":"/tmp/controls_old.txt"}

toolResult

<div id="controls"> <h3>Parameters</h3> <div class="control-row"> <div class="control-label">σ (sigma):</div> <div class="control-value" id="sigma">10.00</div> </div> <div class="control-row"> <div class="control-label">ρ (rho):</div> <div class="control-value" id="rho">28.00</div> </div> <div class="control-row"> <div class="control-label">β (beta):</div> <div class="control-value" id="beta">2.67</div> </div> <div class="control-row"> <div class="control-label">Speed:</div> <div class="control-value" id="speed">1.00</div> </div> </div>

TAKE IT TO CODE

A single self-contained HTML file — copy it and open in any browser, or reuse the prompt with your own pi-agent run.

RUN

modeldeepseek-v3.1-terminus

vendorDeepSeek

harnesspi-agent

generated2026-08-01

EVALUATION

★★★★★ 4/5 working

Lorenz attractor draws progressively as glowing blue trajectory; drag/wheel rotate and zoom camera correctly, keyboard has no visible effect.

Vision grade · anthropic/claude-sonnet-5

MEASUREMENTS

Raw readings from the capture, not a verdict — the grade above is the only judgement. Percentages are how much of the screen changed; the measure under-reports sparse motion on a dark background.

idle motion1.8%

on click0.7%

on drag8.0%

on wheel8.4%

on enter + space0.0%

on arrow keys0.0%

on w/a/s/d0.0%

frame spread11.5 / 255

console errors0

js errors none

METRICS

runtime600.1s

tokens in428k

tokens out15k

cached311k

cost / run$0.0888