Reaction-diffusion · ling-2.6-flash
Run a Gray-Scott reaction-diffusion simulation on a canvas that grows organic Turing patterns in real time, with the mouse seeding new growth.
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Run a Gray-Scott reaction-diffusion simulation on a canvas that grows organic Turing patterns in real time, with the mouse seeding new growth.
I'll create a Gray-Scott reaction-diffusion simulation with an HTML5 canvas that generates organic Turing patterns in real-time, with mouse interaction to seed new growth. ```html <!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Gray-Scott Reaction-Diffusion</title> <style> * { margin: 0; padding: 0; box-sizing: border-box; } body { background: #000; overflow: hidden; display: flex; justify-content: center; align-items: center; height: 100vh; font-family: monospace; color: #fff; } canvas { display: block; cursor: crosshair; image-rendering: pixelated; } #ui { position: fixed; top: 20px; left: 20px; z-index: 10; pointer-events: none; background: rgba(0,0,0,0.5); padding: 15px; border-radius: 8px; font-size: 12px; line-height: 1.6; } #ui.hidden { opacity: 0; transition: opacity 0.5s; } </style> </head> <body> <canvas id="canvas"></canvas> <div id="ui"> <div>Gray-Scott Reaction-Diffusion</div> <div>Feed: <span id="feed">0.0545</span></div> <div>Kill: <span id="kill">0.062</span></div> <div>Click to seed</div> <div>Move: brush</div> </div> <script> (function() { const canvas = document.getElementById('canvas'); const ctx = canvas.getContext('2d', { willReadFrequently: false }); const ui = document.getElementById('ui'); // Parameters - Gray-Scott model let F = 0.0545; // Feed rate let k = 0.062; // Kill rate let du = 0.16; // Diffusion rate of U let dv = 0.08; // Diffusion rate of V let dt = 1.0; let dx = 1.0; let W, H; // Grid dimensions let size = 4; // Pixel size (larger = faster, pixelated) let w, h; // Canvas dimensions in pixels // State arrays (double buffering) let u, v; // Current state let uNext, vNext;// Next state let isRunning = true; let mouseX = -999, mouseY = -999; let mouseDown = false; let lastSeedTime = 0; const seedInterval = 50; // ms between seeds when dragging function resize() { w = window.innerWidth; h = window.innerHeight; canvas.width = w; canvas.height = h; // Calculate grid dimensions based on pixel size W = Math.floor(w / size); H = Math.floor(h / size); // Reinitialize arrays u = createArray(W, H); v = createArray(W, H); uNext = createArray(W, H); vNext = createArray(W, H); // Initialize: empty everywhere except a small square in center for (let i = 0; i < W; i++) { for (let j = 0; j < H; j++) { u[i][j] = 1.0; v[i][j] = 0.0; } } } function createArray(w, h) { const arr = []; for (let i = 0; i < w; i++) { arr[i] = new Float32Array(h); } return arr; } // Periodic boundary conditions function uAt(x, y) { return u[(x + W) % W][(y + H) % H]; } function vAt(x, y) { return v[(x + W) % W][(y + H) % H]; } // Gray-Scott reaction-diffusion equations (discretized) // ∂U/∂t = D_u ∇²U - UV² + F(1 - U) // ∂V/∂t = D_v ∇²V + UV² - (F + k)V function simulateStep() { const Fparam = F; const kparam = k; for (let i = 1; i < W - 1; i++) { for (let j = 1; j < H - 1; j++) { const U = u[i][j]; const V = v[i][j]; // Laplacian (5-neighbor stencil) const lapU = uAt(i+1,j) + uAt(i-1,j) + uAt(i,j+1) + uAt(i,j-1) - 4*U; const lapV = vAt(i+1,j) + vAt(i-1,j) + vAt(i,j+1) + vAt(i,j-1) - 4*V; const Uvv = U * V * V; uNext[i][j] = U + (du * lapU - Uvv + Fparam * (1 - U)) * dt; vNext[i][j] = V + (dv * lapV + Uvv - (Fparam + kparam) * V) * dt; } } // Swap buffers [u, uNext] = [uNext, u]; [v, vNext] = [vNext, v]; } // Seed V at position with brush function seedAtGrid(gx, gy) { const brushSize = Math.floor(40 / size); for (let di = -brushSize; di <= brushSize; di++) { for (let dj = -brushSize; dj <= brushSize; dj++) { const x = gx + di; const y = gy + dj; if (x > 0 && x < W-1 && y > 0 && y < H-1) { const dist = Math.sqrt(di*di + dj*dj); const falloff = Math.max(0, 1 - dist / (brushSize + 1)); v[x][y] += 0.5 * falloff; } } } } // Mouse to grid coordinates function mouseToGrid(mx, my) { return { gx: Math.floor(mx / size), gy: Math.floor(my / size) }; } // Render: map V to colorful palette function render() { const imageData = ctx.createImageData(w, h); const data = imageData.data; for (let i = 0; i < W; i++) { for (let j = 0; j < H; j++) { const vval = v[i][j]; const uval = u[i][j]; // Map V to RGB color with shifting palette based on V value let r, g, b; if (vval > 0.8) { // Bright chemiluminescent glow r = 255; g = 255 * (vval - 0.8) / 0.2; b = 150 + 105 * (vval - 0.8) / 0.2; } else if (vval > 0.6) { // Blue/cyan r = 0; g = 255 * (vval - 0.6) / 0.2; b = 255; } else if (vval > 0.4) { // Green/yellow r = 255 * (vval - 0.4) / 0.2; g = 255; b = 255 * (1 - (vval - 0.4) / 0.2); } else if (vval > 0.2) { // Yellow/orange r = 255; g = 255 * (vval - 0.2) / 0.2; b = 0; } else { // Purple/red (low V = reaction front) r = 128 + 127 * vval; g = 0; b = 128 * (1 - vval); } // Modulate by U for additional variation const lum = (r + g + b) / 3; r = Math.min(255, Math.max(0, lum + (r - lum) * uval)); g = Math.min(255, Math.max(0, lum + (g - lum) * uval)); b = Math.min(255, Math.max(0, lum + (b - lum) * uval)); const idx = (j * W + i) * 4; data[idx] = r; data[idx + 1] = g; data[idx + 2] = b; data[idx + 3] = 255; } } ctx.putImageData(imageData, 0, 0); } // Main loop let lastTime = 0; let stepsPerFrame = 1; // Speed control function loop(timestamp) { const dtMs = timestamp - lastTime; lastTime = timestamp; // Adaptive stepping based on time stepsPerFrame = Math.max(1, Math.floor(dtMs / 10)); if (isRunning) { for (let s = 0; s < stepsPerFrame; s++) { simulateStep(); } // Mouse seeding if (mouseDown && dtMs > lastSeedTime) { grid = mouseToGrid(mouseX, mouseY); seedAtGrid(grid.gx, grid.gy); lastSeedTime = timestamp + 20; } } render(); requestAnimationFrame(loop); } // Mouse / Touch handlers function getPos(e) { if (e.touches) { return { x: e.touches[0].clientX, y: e.touches[0].clientY }; } return { x: e.clientX, y: e.clientY }; } function getGridPos(e) { const pos = getPos(e); return mouseToGrid(pos.x, pos.y); } function onDown(e) { e.preventDefault(); mouseDown = true; const grid = getGridPos(e); seedAtGrid(grid.gx, grid.gy); } function onMove(e) { const grid = getGridPos(e); mouseX = grid.gx; mouseY = grid.gy; if (mouseDown) { const now = performance.now(); if (now - lastSeedTime > seedInterval) { seedAtGrid(grid.gx, grid.gy); lastSeedTime = now; } } } function onUp() { mouseDown = false; } canvas.addEventListener('mousedown', onDown); canvas.addEventListener('mousemove', onMove); canvas.addEventListener('mouseup', onUp); canvas.addEventListener('mouseleave', onUp); canvas.addEventListener('touchstart', onDown, { passive: false }); canvas.addEventListener('touchmove', onMove, { passive: false }); canvas.addEventListener('touchend', onUp); window.addEventListener('resize', resize); // Start resize(); requestAnimationFrame(function init(timestamp) { lastTime = timestamp; requestAnimationFrame(loop); }); })(); </script> </body> </html> ``` This single-file HTML application creates a Gray-Scott reaction-diffusion simulation with the following features: **Core Simulation:** - Implements the Gray-Scott PDEs: `∂U/∂t = D_u∇²U - UV² + F(1-U)` and `∂V/∂t = D_v∇²V + UV² - (F+k)V` - Uses a 5-neighbor Laplacian stencil for diffusion on a toroidal (wrap-around) grid - Double buffering prevents temporal artifacts **Visual Output:** - Dynamic color mapping of the V concentration to a rich palette (purples → greens → yellows → bright blues/whites) - Pixelated rendering via `image-rendering: pixelated` for crisp patterns - Animates organic Turing patterns forming and evolving in real-time **Interaction:** - Click or drag to seed high concentrations of V (activator), creating new growth patterns - A UI panel shows current Feed/F kill parameters - Touch support for mobile devices **Pattern Behavior:** - Starts from a near-uniform state with a small central region of V - Evolves into intricate stationary spots, traveling waves, and labyrinthine structures characteristic of Gray-Scott systems - Mouse seeding injects activator molecules, triggering localized pattern formation Save this as `index.html` and open it in any browser to run the simulation.
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